Tied at 1 with 9:39 gone in the second period, Niklas Kronwall hooked Ott on a breakaway and Buffalo was awarded a penalty shot.
The Sabres captain went left, and Gustavsson stayed with him.
''I didn't actually think he was going to go that way because that's the way he went when he had the first opportunity, but he did,'' Gustavsson said. ''I tried to be patient and follow him and lucky enough, he didn't score.''
Cody Hodgson scored Buffalo's goal. The Sabres are winless since a victory in interim coach Ted Nolan's first game on Nov. 15.
The Red Wings were playing their third game in four nights but appeared the fresher team against the struggling Sabres.
''We decided to play a really solid game tonight,'' Franzen said. ''We talked about being patient, not giving up too many chances for the other team. I think we stuck to the plan pretty good and finally managed to get the win.''
Gustavsson was a difference maker, with several key stops on Buffalo's two third-period power plays, including a save on Drew Stafford's between-the-legs effort.
''He's a gamer,'' Franzen said. ''He battles like crazy out there. He can really play the puck and read the play so we've got a lot of confidence in him.''
Detroit improved to 7-3-1 on the road. Buffalo has lost 11 of 13 home games.
Ryan Miller made 32 saves for the Sabres. He is 2-8-2 against Detroit in his career.
''We can't just get by and feel like 1-1 is good,'' he said. ''We have to go for it at home, especially with a team playing three in four nights.''
The Sabres took a 1-0 lead 11:58 into the game on a highlight-reel goal from Hodgson. Stafford intercepted a clearing attempt and passed in the slot to Hodgson, who forced Gustavsson out of the crease goal and then, with his body behind the goal line, used his backhand to tuck the puck into the net.
Detroit controlled play for most of the first period but Miller made 14 saves, including a left pad save on Joakim Andersson in the closing seconds, to maintain the Sabres' lead.
''He's really good,'' Detroit coach Mike Babcock said. ''Him and (Boston goalie Tuukka Rask) to me are two of the best skating goalies in the league. They look like they put no effort into it. They're just always in the right place. I thought he made some really good saves.''
It took less than a minute of second period play for Detroit to tie it. Alfredsson found Darren Helm in the slot, and Helm spun away from Tyler Ennis to lift a backhand past Miller.
''I knew there was someone on my back there,'' said Helm, who's scored in three consecutive games. ''I just tried to get into the middle and get a shot off. I kind of surprised myself.''
The go-ahead goal came on a power play when Franzen's shot deflected off Sabres defenseman Alexander Sulzer and past Miller. Zetterberg assisted on the tally and improved his point total to 28, good for second in the NHL.
Alfredsson scored an empty-net goal to clinch the win.
It was the sixth game pitting Ryan Miller against his younger brother Drew, who is 5-1 against his older sibling.
''He played really well,'' Drew Miller said. ''A close win for us where he plays well but we still wins is kind of a bonus for me.''
NOTES: The Sabres wore their gold alternate jerseys for the first of 10 scheduled games this season... Detroit RW Todd Bertuzzi missed his second game with an upper body injury. ... The Red Wings were without Pavel Datsyuk, who is recovering from a concussion after an elbow from Jared Cowen on Saturday night in Detroit. He will be out indefinitely.