The full-back curled in a superb free-kick to put his side 2-1 up after Ciro Immobile had drawn Lazio level.
In doing so, former Lazio player Kolarov became only the second player in the history of the rivalry to score for both teams in a derby clash.
Arne Selmosson is the only other player to have done it and that was back in 1958.
Kolarov, quoted on Roma’s Twitter page, said: “It’s 60 years since anyone did it. I always try to give my best.
“I knew I would have a chance to score in the derby for Roma as well. I’m very pleased.”
Lorenzo Pellegrini opened the scoring for Roma just before half-time but his effort was cancelled out by Immobile in the 67th minute.
Kolarov’s strike regained the advantage before Federico Fazio’s header sealed a second successive win for the Giallorossi, who started the game 10th having taken just eight points from their first six matches.
“It was important to win for ourselves,” Kolarov said. “I’ve always said that we’re a great team and today we went out there and did what we had to do to win. I’m happy for the fans, for myself and for the team.”
Roma captain Daniele De Rossi stressed the importance of ensuring his side did not get beaten by their fierce rivals.
“If we had lost it could have cut our legs out from under us. Winning gives us more belief. We will celebrate but will have to put it to one side,” De Rossi told Roma’s website.
“There was a lot of pessimism, a bit of uncertainty between the squad and the Roma environment. Losing the derby today would have been a disaster, it would have been very tough to come back from.”
Roma’s victory moves them to within a point of Lazio, whose manager Simone Inzaghi was not happy with the application he saw from his side, believing their rivals had a greater edge.
“Roma had more malice, they believed more, despite having scored on three set-pieces. We had reached a draw but then we conceded a goal from a free-kick that condemned us,” Inzaghi told Sky Sport.
“We had a good 20 minutes but we should have paid more attention. If you concede three goals like that in a derby, you’re likely to lose it.”