The 22-year-old eased to a 6-1 7-6 victory over Davide Sanguinetti to level the round-robin tie at 1-1 after Francesca Schiavone had beaten Gisela Dulko 6-1 6-3 in the opening match of the mixed team event.
For Coria, runner-up at the French Open last year, it was his first victory since he lost in the second round of Wimbledon in June.
Coria was forced to have shoulder surgery in August, which kept him off the tour for almost four months.
Having lost all three of his matches on his return in November at the Masters Cup in Houston, Coria looked more like his usual self on Sunday as he eased to victory against the 110th ranked Sanguinetti.
The Italian also had to deal with an ankle injury, which he picked up while stretching for a backhand in the second game of the match.
After taping his ankle at the next change of ends, Sanguinetti battled on and though he dropped the first set, he led 4-2 in the second before Coria recovered to clinch victory.
The win was especially sweet for Coria, who was due to participate in the 2002 tournament but was prevented from playing after he received a seven-month ban for returning a positive drugs test for nandrolone.
Coria will team up with Dulko in the mixed doubles against Sanguinetti and Schiavone in the deciding rubber.
Earlier, Schiavone proved too consistent for Dulko as she wrapped up victory in one hour, five minutes.
The Argentine, who beat Martina Navratilova at the French Open and Wimbledon last year, made 46 unforced errors.
