With time winding down and Tampa Bay goalie Dwayne Roloson scrambling back after heading for the bench, Vanek scored his third goal of the game by firing a shot from just inside the blue line to seal a 4-2 victory on Tuesday.
Buffalo moved into seventh place in the Eastern Conference, a point ahead of the idle New York Rangers, and five up on ninth-place Carolina with five days left in the season.
"I wasn't going to mess around with that," Vanek said of the goal he scored with 14 seconds remaining. "Any time you can get that extra one to give you a little bit more cushion, it doesn't matter how much time is left, you'll take it."
Vanek's goal relieved the tension from a game which became tight 17 seconds into the third period, when Vincent Lecavalier put a scare into the Sabres by cutting their lead to 3-2.
"We made one mistake against that top line," Vanek said. "But we didn't give them much after."
Improving to 7-1-2 in its past nine games, Buffalo now needs one point in either of its final two games or a Hurricanes loss to clinch a postseason berth. The Sabres' victory also knocked the Toronto Maple Leafs out of contention.
Ryan Malone also scored for the Lightning, who had a five-game winning streak snapped and lost for the first time in four road games. The loss leaves fifth-place Tampa Bay all but mathematically out of the hunt to open the playoffs at home next week.
The Lightning (44-25-11) can no longer catch Southeast Division-leading Washington, and they also fell three points back of fourth-place Pittsburgh, which defeated New Jersey later in the evening.
"We want to get momentum going into the playoffs, playing the right way," Lightning forward Martin St. Louis said. "We've done that so far in the last four or five games. Tonight's second period got away a little and it cost us."
The Sabres rallied for three goals after Malone opened the scoring at 13:53 of the first period.
Vanek tied it three minutes later by tipping in Jason Pominville's shot during a two-man advantage.
He then scored the go-ahead goal eight minutes into the second period with a nifty play in front. Pominville set it up by digging the puck out along the right boards and feeding a pass into the front, where Vanek created space for himself by first shoving defenseman Mattias Ohlund from behind. Taking the puck on his forehand, Vanek then went backhand and flipped a shot over Roloson's right pad.
Connolly provided the Sabres a 3-1 cushion by scoring with 6:14 left in the second period, but the Lightning proved they weren't done yet.
Intercepting Connolly's clearing pass inside the Sabres zone, St. Louis fed a wide-open Lecavalier, who silenced the hometown fans, who were still getting back into their seats after the second intermission.
Sabres coach Lindy Ruff could sense his team growing tentative.
"I said, 'Let's not be scared. Let's go out and play,"' Ruff said. "And one guy yelled, 'I'm not scared."'
Vanek enjoyed his sixth career three-goal game and took over the team lead with 31 goals -- one more than Drew Stafford. Vanek has now scored 30 goals four times in his six-year NHL career.
And he set up the final goal himself by stripping St. Louis of the puck in the neutral zone and then skating in up the right wing before slapping the shot into the wide-open side.
Vanek's clutch production pleased Ruff, who has spent the past few months demanding more from his star players as the Sabres have climbed into contention after being as many as 10 points out in mid-January.
"He played a very good game for us," Ruff said. "Van was big again tonight. Our big players are making a difference, and that's important."
- Lightning D Victor Hedman left the game in the second period and did not return with what the team called a lower body injury. Coach Guy Boucher listed Hedman as day to day.
- Lecavalier wore a visor after requiring three stitches to close a cut over his left eye on Sunday, when was accidentally high-sticked by Chicago's Michael Frolik in the second period of a 2-0 win.
- Sabres D Jordan Leopold will not require surgery to repair a broken left thumb. He's been cleared to begin practicing, and could return within two weeks.