01/07/2014 10:55 EST | Updated 03/09/2014 05:59 EDT

Martin St. Louis nets winner as Tampa Bay beats Winnipeg Jets 4-2

WINNIPEG - For a guy who just played a key role in winning a hockey game Tuesday night, Martin St. Louis was still not a very happy fellow.

It was understandable perhaps, after the veteran forward was passed over by his own general manager for a spot on the Canadian Olympic team.

"I'm happy we got the win," he said after his two third-period goals nailed down the 4-2 victory over the Winnipeg Jets, their fourth loss in a row. "For Team Canada, you guys can imagine how I feel, obviously, I'm extremely disappointed and I'll just leave it at that."

St. Louis scored the winner in the third period then capped it with an empty-net goal.

The Jets were outshot two-to-one for most of the game and finished with just 14 shots on goal to 33 for the Lightning, but still managed to go into the third tied 2-2.

That was no consolation for Winnipeg coach Claude Noel.

"Certainly for us this is probably the worst we played," he said. "It was an empty game. We got very little production in any facet of the game. I don't have the answers."

The Jets scored two power-play goals and had managed to kill four of the chances they handed Tampa, until St. Louis tipped in Victor Hedman's shot from the point at 8:39 of the third on a fifth power play.

Valtteri Filppula and Ondrej Palat also scored for the Lightning (26-13-4). Olli Jokinen and Dustin Byfuglien scored for the Jets (19-22-5).

"It would be hard to pick anybody who was good in the game," said Noel.

Jets goalie Ondrej Pavelec agreed.

"It was embarrassing," he said. "The way we play, we can't expect to be a success, that's for sure."

He said they managed to stay in the game but "I don't think we showed up tonight," adding "we got what we deserved."

Cooper was pleased at the way the whole team responded after a tough day when only Steven Stamkos from the Lightning got the nod for a spot on the Canadian Olympic team.

"The guys still found a way to come into a hostile environment here — this is a tough place to play on the road — and I thought we just played an outstanding road game."

Tampa got off to a quick start. Filppula deked past Byfuglien in front of the Winnipeg net to fire one past Pavelec at just 1:20 with the first shot of the game for the Lightning.

But the Jets made good on a five-on-three later in the first. Mark Scheifele fed a pass across the Tampa crease and Jokinen popped it behind backup netminder Anders Lindback before he could recover.

A slashing penalty to Filppula and a delay of game for Lindback (served by B.J. Crombeen) set up the scoring opportunity.

The Jets managed only two shots in the first period to Tampa's five and were outshot 12-7 in the second as well.

But Byfuglien still put them ahead on another power play early in the period, snapping one past Lindback on the short side off a drop pass from Blake Wheeler.

Things got chippier as the period progressed and tempers flared. Tampa had a couple of power-play chances but managed only one shot on both combined.

Shortly after the last, however, Palat tied things up on a pass from Nikita Kucherov after a breakaway by Alex Killorn at 15:37.

The Jets penalty kill finally buckled in the third on Hedman's shot from the point that St. Louis tipped in from Pavelec's glove side.

Frustration boiled over again late in the third and gloves and sticks littered the ice after a clash around the Tampa net that saw four players sent to the box. The game basically ended with a fight between Evander Kane and Eric Brewer.

Winnipeg had lost their last three going into Tuesday's game, while Tampa had a five-game road winning streak snapped last Sunday by the Edmonton Oilers.

Notes: Pavelec picked up a rare netminder's assist on Byfuglien's goal. For whatever reason, Tampa has had trouble beating Winnipeg. The Jets won their first meeting of the season Dec. 7 in overtime and going into Tuesday's game had won the past four against Tampa. They still have a record of 7-3-2 against the Lightning since moving from Atlanta in 2011.