David Goffin was serving for the match before Troicki mounted a comeback for a 1-6, 3-6, 7-6 (7-5), 6-4, 6-4 victory in about 4 hours. Djokovic, the world No. 1, rolled over Olivier Rochus 6-3, 6-2, 6-2 in 99 minutes.
Serbia, which won the Davis Cup in 2010, is one win away from a berth in the 2013 quarterfinals. A win by Troicki and Nenad Zimonjic in Saturday's doubles match against Belgians Ruben Bemelmans and Steve Darcis would secure that.
If Bemelmans and Darcis win, however, the series would be decided in Sunday's reverse singles when Djokovic takes on Goffin and Troicki goes against Rochus.
The series winner draws the survivor of a series between Brazil and the United States in the quarterfinals.
Goffin was 3-0 in previous Davis Cup matches and built a huge lead with seven breaks to get to 5-4 of the third set. But he committed a string of unforced errors that allowed Troicki to even the set and win the tiebreaker. Goffin had additional chances the rest of the way, with six break opportunities, but Troicki finished all three of his chances for the win.
Djokovic won nearly 80 percent of the points on serve and didn't face a break point. He had a mere 24 unforced errors against 59 winners -- including 20 aces -- in showing the same form that allowed him last Sunday to capture his third consecutive Australian Open title.