Wellwood scored from in close off a left-circle pass from Blake Wheeler.
Wheeler also scored for the Jets, who had lost seven straight games at Tampa Bay dating to the team's days in Atlanta. Ondrej Pavelec finished with 30 saves.
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 a personal 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 all eight games during the stretch.
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 a goal in his previous 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 the second.
Winnipeg defenseman Dustin Byfuglien was back in the lineup after missing the previous 16 games because of a knee injury and assisted on Wellwood's goal. Jets center Alexander Burmistrov also returned after sitting out two games with concussion-like symptoms.
Notes: Stamkos assisted on Hedman's goal. ... Tampa Bay D Marc-Andre Bergeron (back) and RW Adam Hall (torn forearm muscle) both have resumed practicing. ... Slater stopped a 26-game stretch without an assist ... Lightning rookie RW Brett Connolly, who has gone 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 present.