He'd worn the C, and worn it well, so he knew what he was talking about. "The advice I gave him was to come to work with a good attitude day in and day out and be hard-working and be consistent with it," Sittler recalls. He'd done the same himself in setting a club record with 389 goals in the process.
Sundin had 386 going into a game against the visiting Boston Bruins on Tuesday night, and Sittler will be happy for him when he gets No. 390.
"Mats is very well-liked by his teammates, the media and the fans," says Sittler. "He's been the cornerstone of the franchise for a number of years.
"It was only inevitable that it was going to happen. The reason it didn't happen earlier was that players didn't have the longevity Mats or I had in Toronto."
Sittler is still in Toronto, of course. He's 56 now and a community ambassador for the team with special interest in the Leafs' Fund. Sundin, 36, lends a hand on projects such as the recent Have A Heart dinner.
"We'll chit-chat," says Sittler. "The hockey side of things, I don't need to say much about that to him.
"He's been such a consistently good player, and I admire that he's out in the community doing things, too. I think he realizes that he can make a difference in peoples' lives by being out there and giving his time."
They are from such different hockey eras.
Sittler played at a time when the Leafs had to scrap with the Big Bad Bruins and then the Broad Street Bullies. A hook here, a hold there, a brawl everywhere.
"It's a lot different now," Sittler says. "Back then, there were a lot of games that not only a brawl broke out where everybody was squared off, but there were bench-clearing brawls.
"As a player in the 1970s, you were looked upon to defend yourself. The better players, as much as they were targets and had players to look out for them, it wasn't unheard of for them to fight some of their own battles."
There was no instigator penalty as is the case today.
"The NHL has done a good job of changing things and, with the influx of players from other countries with lots of skills, the game has changed to adapt to the good points in the way they play," says Sittler. "That's the evolution of the game."
As Sundin has done all these years later, leading by example was Sittler's approach.
"A strong work ethic and how you conducted yourself off the ice - those things were important," he says. "I was vice-president of the players' association and captain of the team so communication with coaches and management was a key part of it all.
"I was fortunate to have Jim Gregory as my GM and coaches like Red Kelly and Roger Neilson. The other thing was I was fortunate to have a good cast around me like Tiger Williams, Lanny McDonald, Borje Salming and Pat Boutette - guys who were leaders themselves. To be a captain, it's important that you get that support from your teammates."
Sundin feels he gets it.
Sittler was a centre. So is Sundin. Both were named all-stars by the league, both played starring roles in international triumphs, both earned great respect from their teammates, and neither has won the Stanley Cup.
But they're different, too.
Sittler was more of a big-time scorer than Sundin. Sittler had eight consecutive seasons in Toronto with more than 35 goals. Sundin has done it three times for the Leafs.
The six-foot-five, 230-pound Sundin is more physically powerful than was Sittler in the six-foot, 190-pound frame of his playing days, and he plays a two-way game at a level few can match.
Sundin is single, while Sittler helped raise a family during his playing career. His wife Wendy died in 2001.
Sundin takes off to a cottage in northern Sweden for the summers, while Sittler was around most of the year - and still is.
Sundin was born in 1971, which was Sittler's first season with the Leafs. Sittler would score 389 goals in 844 games in the blue and white. Sundin had 386 in 884 games with the team before the game against the Bruins.
Sittler's most sensational performance was on the night of Feb. 7, 1976, when he scored six goals and assisted on four during an 11-4 win over Boston in Maple Leaf Gardens to set the NHL record, which still stands, for most points in one game.
That wasn't all he did that year: he scored five goals in an 8-5 playoff win over Philadelphia, and he still owns a share of the single-game playoff record; and he scored the tournament-ending overtime goal for Canada against Czechoslovakia in the inaugural Canada Cup.
Sundin was so highly regarded by Swedish hockey executives that they made him captain of the team that won 2006 Olympic gold.
Current teammate Pavel Kubina was on the Czech team in that tournament. Facing Sundin was a huge challenge.
"Mats is a very strong guy," says Kubina. "He uses that to his advantage in the corners.
"He waits for the hit and bumps you out, and he goes to the net to score goals like he did in our last game."
Against Edmonton last Saturday, Sundin got the puck behind the Oilers net, held off a checker with smart positioning and muscle, darted into the crease while somehow maintaining his balance while being pushed, and stuffed the puck past goaltender Dwayne Roloson. Few other players, if any, would be capable of duplicating that goal.
"He has so much talent and he's so smart," says Kubina. "It's difficult to play against him, especially with the new rules where you can't hold or hook.
"He can do pretty much everything out there, and he's a great leader on a team. I'm just happy I'm playing on the same team as him now."
Sittler was in turmoil during parts of his last two years as a Leaf as Punch Imlach traded away players and sucked the potential out of a lineup that had appeared to be on the verge of great things. Sittler removed the C from his sweater in protest at one stage. Things settled down for a while, but he was traded to Philadelphia in January 1982. He played a season in Detroit before calling it quits in 1985. He was inducted into the Hockey Hall of Fame in 1989.
Sundin will eventually join him.
"He's one of the best," says Alex Steen, one of the young Toronto players who look up to the captain. "I have the privilege of sitting next to him in the dressing room and get to see first hand how he is.
"You don't really know how much of an effect he has on the team and how much of a leader he is until you get the chance to play with him. The way that he keeps performing day in and day out is unbelievable.
"He's the hardest-working player on the team. When he's at the rink he's pretty serious about the team and his hockey. Off the ice, he's pretty relaxed and likes to have a good time."
Teammate Wade Belak defines Sundin as "a very humble guy."
"He's a good person - not an ounce of arrogance at all. He's a super-nice guy. There are a few hockey players, not on this team but around the league, who have a bit of an ego, cockiness to them, but not Mats.
"He's a fairly even-keeled guy. Very humble. Good upbringing. He's going for the record and we're all pulling for him because he's a really good guy and he deserves it."
Sittler will shake his hand and congratulate him with sincerity.
"Mats has been and is a good captain for the Leafs," he says. "He's taken on the responsibilities seriously and has done an admirable job.
"He knows the history and tradition of the Leafs and the responsibility that comes with being captain - dealing with the media, being out in the public and also being a good role model for kids and teammates. Mats has had a very consistent career."