"Their goaltender stoned us, basically," Boucher said. "We had tons of quality, quality scoring chances and we couldn't bury them. We did enough to win this game. It didn't turn our way."
Wellwood scored from in close off a left-circle pass from Blake Wheeler.
"That's a nice feeling, getting a goal," Wellwood said. "You know there's an empty net to put it in, which is even better."
Wheeler also scored for the Jets, who had lost seven straight at Tampa Bay -- dating to the franchise's time in Atlanta.
"We had a lot of energy, and I think we were willing to play 65 minutes if we needed to, plus a shootout if it had to go that far," Wheeler said. "I think we're just dedicated right now."
Hedman tied it 1-all at 10:34 of the third from the low left circle after taking a nifty neutral zone touch pass by Martin St. Louis. The defenseman snapped his 25-game goal drought, dating to Oct. 22 against Buffalo.
St. Louis has 10 assists and 13 points during an eight-game point streak. The right wing has at least one assist in every game of the spurt.
"We deserved better," St. Louis said. "There's going to be games that we probably don't play as good and get two points. So you can't get too down."
Wheeler skated down the slot and put the Jets up 1-0 with 15.2 seconds to go in the second on the rebound of Jim Slater's shot from the top of the left circle. Wheeler hadn't scored in seven games.
Stamkos hit the outside of the post on the rebound after Pavelec stopped St. Louis' shot midway through the second. The Lightning outshot Winnipeg 15-7 in that period.
"I thought Pavelec was good when he had to be," Jets coach Claude Noel said.
Winnipeg defenseman Dustin Byfuglien, back in the lineup after missing 16 games because of a knee injury, assisted on Wellwood's goal.
"It went pretty smooth, and I feel great right now," said Byfuglien, who logged 25 minutes, 36 seconds of ice time. "It feels good to get right back on the (score) sheet and try to do as much as I can."
Jets center Alex Burmistrov also returned after sitting out two games because of concussion-like symptoms.
"We battled hard," Pavelec said. "That's exactly what you want on the road."
Stamkos assisted on Hedman's goal. ... Jets RW Bryan Little had five shots, but failed to score a goal for the 14th consecutive game. ... Tampa Bay D Marc-Andre Bergeron (back) and RW Adam Hall (torn forearm muscle) both have resumed practicing. ... Slater snapped a 26-game stretch without an assist ... Lightning rookie RW Brett Connolly, pointless in 16 consecutive games, was a healthy scratch. ... With the trade deadline nearing, Pittsburgh, Chicago, Dallas, Montreal and Detroit were among the teams with scouts in attendance.