Holt was twice denied by the woodwork in the first half and had several other opportunities before finally making one count in the 62nd minute after good work from Korey Smith and Wes Hoolahan.
It was the first goal Holt had scored in six games and it helped Norwich bounce back from Tuesday night's defeat at Doncaster while condemning Preston to a fourth successive loss.
City made a promising start and Hoolahan, still without a goal this season, let fly from 25 yards but failed to find the target.
Moments later, the visitors had another opening. This time a cross from Simon Lappin, back in the side at the expense of Anthony McNamee, found on-loan defender Leon Barnett but he headed wide under pressure.
Preston, on the back of five defeats in six league games, had their first chance in the 10th minute although Paul Parry could only scoop the ball over the bar after goalkeeper John Ruddy had partially punched away Paul Hayes' corner.
Norwich responded with a couple of corners of their own and from both deliveries by Lappin, captain Grant Holt and Barnett could not force goalkeeper Andy Lonergan into action.
Jon Parkin, with two goals in his last two games, forced a smart save from Ruddy in the 18th minute before Hayes, released by Norwich as a youngster, headed wide as Preston threatened.
The Canaries then came closest to breaking the deadlock in the 21st minute when Holt headed another Lappin corner against the crossbar from close range.
Preston were awarded a free-kick in a dangerous position seven minutes later but Sean St Ledger's looping header was dealt with by Ruddy and Chris Martin fired over from 25 yards at the other end.
Norwich finished the first half on top and Holt twice came close to giving his side the lead.
First he glanced a Lappin cross wide from 12 yards before his 12-yard volley crashed against the post in injury time.
Preston made a change at the break with Iain Hume, signed on loan from Barnsley, replacing Keith Treacy for his debut.
The Canada international nearly made an immediate impact when he headed a cross from Darel Russell, facing his former club for the first time since his summer break, wide from 12 yards.
Holt headed a chance wide before Hume crossed for Parkin but the giant forward headed wide from six yards while Ruddy had to tip over a long-range effort from Adam Barton.
Russell then nodded a corner from substitute Danny Mayor over the bar and then Norwich took the lead in the 62nd minute, Holt netting from 12 yards after being played in by Smith.
Martin and Hoolahan had chances to put the result beyond doubt but Norwich comfortably held on.