A Jon Daly penalty and Stuart Armstrong strike cancelled out Paul Dummett's opener to give United a 2-1 half-time lead which evaporated when Steven Thompson netted his fourth goal in three games after 50 minutes.
Marc McAusland put the Buddies in front after 65 minutes before United defender Brian McLean was sent off and a rare David van Zanten goal after 78 minutes completed victory for the visitors.
Barry Douglas' 90th-minute free-kick was mere consolation as United's winless run at Tannadice was extended to 10 games.
"It's a fantastic three points for us and a terrific way to finish 2012," Lennon said. "The key thing for us and our success was the continuous work-rate for the players individually and, more importantly, as a team."
A second away win of the season took the Buddies to 24 points in a congested table, one behind United, who remained eighth after their winless run was extended to four matches, during which they have conceded 11 goals.
"We're just going to ask the boys for one last push before a welcome break and look for the same commitment, the same work ethic and the same quality," Lennon added.
"I don't know if that break's coming at a good time for us or not."
- Sports & Recreation