Paul Dummett, Steve Thompson, Marc McAuskland and David van Zanten scored for the Buddies with Jon Daly, Stuart Armstrong and Barry Douglas replying for the hosts.
"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."
United have not won at home since the August defeat of Dundee and assistant manager Paul Hegarty said: "Scoring three goals and coming away with nothing is disappointing.
"The goals we lost were poor by our standards and it told in the end because we lost the three points. We've had too many games like that at home this year. We can't explain it."
Unless Sean Dillon recovers sooner than expected from a thigh injury, striker Daly is likely to drop back to centre-back.
Hegarty added: "He's a quality striker and we'd rather have him up front, but we had to put Jon back (after McLean's dismissal)."