Two goals from Kenny McLean, the second a penalty, either side of a Paul McGowan strike had put St Mirren ahead on three occasions, but each time St Johnstone hit back.
In-form Steven MacLean, former St Mirren man Nigel Hasselbaink and substitute Rory Fallon responded, the latter after the visitors had had Frazer Wright sent off, before Thompson's strike finally earned a 4-3 success for the home side.
"The players showed great character, great strength and good quality football," said Lennon.
"We've got a reputation as a side that likes to pass the ball and we've been ramming that down their throats from the first day we came here, but for whatever reason they're now matching that with work ethic and determination.
"I must compliment the players and the character they showed."
After a difficult start to the season, St Mirren have now picked up seven points from their last three matches and find themselves 15 points clear of bottom-placed Hearts.
They could have made things easier for themselves on Saturday afternoon had Jim Goodwin not missed a penalty which would have put them 3-2 up.
"Myself and my staff have never changed. Even in the difficult times we tried to keep a level head in the way we worked on a daily basis," Lennon said.
"But something has dropped in that dressing room, there's a clear unity, there's a clear team spirit there, and not just the 11 out there on the pitch.
"It's a great environment to be in."
St Johnstone manager Tommy Wright was understandably disappointed to lose the match after his side had levelled on three occasions.
"To score three times away from home and come out on the wrong end of a result, I'm extremely disappointed for the players," said Tommy Wright.
"It was an entertaining game, but I think at times it was too open. We showed a lot of character to come back every time they scored, and particularly when we went down to 10 men, so I've got nothing but praise for the players, and hopefully we can bounce back from that."
Tommy Wright was also disappointed in referee Willie Collum's decision to award the second of St Mirren's penalties, which was scored by McLean, with the subsequent red card for defender Frazer Wright adding to his frustration.
"My instinct is that Frazer's one isn't a penalty, I think he's used his strength to stay in front of the player and nick the ball," he said
MacLean, who had earlier scored his third goal in two games, was stretchered off late on, with the injury a major concern for the St Johnstone manager.
"There's some swelling in his knee, he's landed awkwardly and thought he was all right and played on and there's been a reaction to that," said Tommy Wright.
"We'll just have to wait and see."