Tomas Kaberle had two assists, while Andrew Raycroft stopped 28 shots for the win as the Leafs grabbed sole possession of the eighth and final playoff spot in the Eastern Conference thanks to losses by the Montreal Canadiens and New York Islanders on Saturday night.
Marc-Antoine Pouliot had a goal and an assist for the Oilers, with Steve Staios and Ryan Smyth adding singles.
Edmonton remained six points behind the final playoff spot in the Western Conference with Minnesota still playing at Nashville on Saturday night. The Oilers fell to 0-2-1 on a seven-game road trip that will decide whether they're buyers or sellers at the Feb. 27 trade deadline.
On the night the Leafs honoured their last Stanley Cup champions in 1967, the present-day edition of the hockey club gave the 19,599 fans at Air Canada Centre reason to dream at least of a playoff berth with yet another strong effort. The Leafs forced turnovers with timely forechecking and limited Edmonton's chances with a tight defensive effort, which has become their trademark of late.
The Oilers didn't look like a team fighting for their playoff lives, outskated and outhustled by the Leafs.
Toronto got the only goal in an evenly played first period, Sundin's one-time blast on a power play at 11:59 set up by a beauty of a pass from Kaberle, who was a force all game long.
Pohl made it 2-0 when he deflected a centring pass from Bates Battaglia behind Dwayne Roloson 4:31 into the second period. The Oilers responded 47 seconds later, Staios blasting a shot from the point that beat a screened Raycroft.
It was Pohl again who restored his team's two-goal advantage at 11:24, slipping in a rebound past Roloson after Kilger stripped the puck from Petr Nedved as the Czech centre tried to skate out of the Edmonton zone.
The rookie Pouliot cut the lead to 3-2 when he coolly deked out Raycroft on a penalty shot with 2:09 in the middle period.
But Sundin, with his 25th of the season, stretched the lead to 4-2 midway through the third period with a wrap-around goal that nearly blew open the roof at Air Canada Centre, the Leafs dominating the last half of the game.
The Oilers narrowed the lead to 4-3 on Ryan Smyth's 29th goal with just over a minute left in the third, but that's as close as they got with Raycroft making a huge save as the buzzer sounded to preserve the Leafs' win.
Notes: Prime Minister Stephen Harper was on hand and made a point of meeting '67 Conn Smythe Trophy winner Dave Keon ... Boyd Devereaux (wrist) was a surprise scratch for Toronto ... Oilers GM Kevin Lowe said contract talks with Ryan Smyth's agent Don Meehan that were supposed to take place Saturday have been pushed back, likely to Sunday or Monday in Naples, Fla., where the NHL's GMs are meeting. Meehan has a home in Naples and will also be down for a few days. Smyth is slated to be an unrestricted free agent July 1 ... Leafs GM John Ferguson said contract talks with Darcy Tucker remain "positive," but still no agreement in place. Tucker is also slated for unrestricted free agency.