Martin Skrtel and Luis Suarez hit the woodwork as the visitors looked like they would make it to half-time level, but Craig Bellamy scored with a deflected shot just before the break.
Three minutes after coming on, Holt planted a bullet header beyond Pepe Reina to equalise.
John Ruddy pulled off an instinctive late save from Suarez to deny the Reds.
Suarez had looked certain to snatch victory for the home side but the Canaries keeper tipped the striker's shot from close range over the bar.
The Uruguayan's effort capped a string of spurned chances as Liverpool laid siege on Ruddy's goal in the closing stages.
The 24-year-old had kept his side level in the opening exchanges of the game, too.
Suarez collected Bellamy's pull back and the former Ajax forward struck a first-time shot that was touched on to the post by the inspired Ruddy.
By that time Skrtel had already rattled the crossbar as Liverpool started strongly.
Norwich steadied the ship and created a couple of half chances of their own, but Reina was equal to what Steve Morison and Anthony Pilkington created in front of goal.
Despite being unable to convert their territorial advantage into clear opportunities, Liverpool were far superior and deserved the lead when it came a minute into first-half injury time.
Latching on to a clipped ball over the Norwich defence, Bellamy muscled his way past the remaining Norwich defenders to slot his shot past Ruddy via the heel of Marc Tierney to score his first league goal since returning to the club.
Norwich, stubborn and disciplined throughout, were then rewarded for their second half fearlessness with an equaliser on the hour.
Having been sent on just three minutes earlier, Holt darted between Jamie Carragher and Glen Johnson to emphatically head Pilkington's pinpoint cross beyond a stranded Reina.
The visitors should have been ahead when another Pilkington cross - this time from the left - found Holt again but Reina reacted well to palm away the substitute's header.
Suarez, who waged an ongoing battle with the officials for their failure to award a decision in his favour, was Liverpool's chief goal threat and he promised to restore the home side's lead several times.
Weaving his way into a shooting position, Suarez seemed certain to roll the ball into the bottom corner - but a desperate block by Russell Martin diverted the ball onto the post.
With time running out Andy Carroll, a late replacement for Bellamy, could have been the hero but he snatched at his shot at the far post.
But that accolade will go to Norwich goalkeeper Ruddy, whose stunning save denied Suarez and Liverpool victory.
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