Wolverhampton Wanderers 2 Cambridge United 1
Out-of-form Wolves had been staring down the barrel of a shock defeat when central defender Collins conceded his third penalty of the season in the 41st minute.
Scott Rendell, whose penalty had earned Cambridge their second round win against Weymouth, stroked home his third FA Cup goal of the season to send shockwaves through Molineux and under-pressure manager Mick McCarthy.
Fortunately for McCarthy, he had key-man Michael Kightly on the bench and it was the introduction of the speedy winger in the 60th minute that turned the game in Wolves' favour.
Kightly, who had missed the previous nine games with an ankle injury, took just nine minutes to fire Wolves back on to level terms when he turned home a Matt Jarvis cross from six yards.
The England Under-21 international than floated over a left-wing cross that Collins rose high to head home two minutes from time and make amends for giving away the penalty.
The defeat was rough on Cambridge, who were well worth a draw and second shot at Wolves.
Wolves would have been out of sight by half-time if their finishing had been better.
But a determined Cambridge rearguard and in-form goalkeeper Danny Potter stood firm before Wolves finally broke their resistance in the last 20 minutes.
Predictably, Cambridge had to weather a storm before Rendell stunned Wolves and the fact they were still on level terms when he struck in the 42nd minute owed everything to Potter.
Michael Morrison set the tone for a determined Cambridge display when he bravely blocked a goalbound drive from Jay Bothroyd.
Potter then denied Bothroyd, Darron Gibson and Jarvis, before Wolves were given a warning they failed to heed in the 22nd minute.
Rendell released Mark Convery and he only had Wayne Hennessey to beat, but the Wales international did well to save at his near post.
Wolves continued to pepper the Cambridge goal but to no avail as Stephen Ward was twice frustrated by Potter - the second time with a stunning one-handed save.
Potter's heroics paid dividends four minutes before half-time when Cambridge were awarded a somewhat controversial penalty.
Collins lost control of the ball on the edge of the area and it was picked up by Convery.
When Convery tried to whip the ball back into the area it was blocked by Collins and referee Kevin Friend ruled that he had used his arm to stop the ball.
It led to a furious reaction by Wolves, but Rendell was not phased and he drilled his spot-kick over the outstretched left hand of Collins.
Cambridge's lead should have been short-lived but Andy Keogh saw his 44th minute header cleared off the line by Mark Albrighton after a cross from Kevin Foley.
Fortunately for Wolves they had Kightly to come riding to the rescue, but it was a perilously close shave for McCarthy.