Conor Newton added a second in the 71st minute, just after the dismissal of Partick right-back Stephen O'Donnell for a second caution, and Thompson struck again in the final minute to put an emphatic gloss on the scoreline for St Mirren.
It was referee John Beaton's decision not to award a spot-kick with the game poised at 1-0 that was the talking point, however, the ball seeming to clearly strike St Mirren captain Jim Goodwin's hand in the area from a Kallum Higginbotham shot.
"That was miles away from me," said Lennon. "Although in saying that, the 4,000-odd in the Jackie Husband stand seemed to think it was [a penalty]!
"But if you say it looks like a penalty then we've maybe rode a wee bit of luck there.
"But I thought the players thoroughly deserved the maximum points in terms of what they brought to the game, in terms of their discipline, their desire to see that out and their patience.
"I must give Thistle a great deal of credit. They caused us a lot of problems first time around and a lot of thought went into the game plan right from last week.
"They're a team that's well-respected, but it's about turning their strengths around into strengths for us, and I think that's what we did."