The Canaries’ substitute sent a thumping header past Pepe Reina in the 60th minute, cancelling out Craig Bellamyâ€™s opening strike on the stroke of half-time.
Liverpool were left to rue their inability to convert opportunities on goal, while Norwich goalkeeper John Ruddy produced a spectacular save in the final minute of the game to deny Luis SuÃ¡rez.
The home side made a strong start and could have been three goals up within the opening 10 minutes.
The first chance came when Charlie Adamâ€™s corner was met by Martin Skrtel – but the centre-half headed onto the crossbar and Norwich were able to scramble the ball clear.
Moments later SuÃ¡rez gained possession with his back to goal and managed to swivel 180 degrees, darting past disorientated defender Leon Barnett and unleashing a shot into the side-netting.
And the Urguayan was involved in Liverpoolâ€™s next attack soon after. Adam struck a mesmerising cross-field pass to Bellamy, who sprinted to the by-line and delivered a delicious cross into the penalty area – but goalkeeper Ruddy was on hand to push SuÃ¡rez’s effort round his right post.
In an increasingly open game, Norwich were able to mount an attack of their own. A long ball found Wes Hoolahan, who managed to barge his way past two Liverpool defenders and unleash a fierce drive which Reina parried clear.
The visitors enjoyed the occasional flurry into the Liverpool half but the home side were dominant.
Stewart Downing, who had a quiet evening on the right wing, sent a floated cross towards SuÃ¡rez but the forward failed to put enough power behind his headed attempt and Ruddy calmly collected the ball.
But the Liverpool pressure did pay off one minute into first half stoppage time.
JosÃ© Enrique’s direct pass caused confusion amongst the Norwich rearguard, with Bellamy collecting possession and slotting the ball into the net, courtesy of a deflection off the lunging Marc Tierney.
After they made the breakthrough, Liverpool should have pressed on and converted their dominance into more goals.
However, Norwich manager Paul Lambert made a key tactical change when he introduced Holt with half an hour remaining, opting to switch to a conventional 4-4-2.
The move paid dividends immediately as the presence of the prolific Holt produced an error from Reina.
Anthony Pilkington countered on the right, surging past Enrique and curling a ball into the area which tempted Reina off his line. The Spanish goalkeeper failed to reach the ball before Holt, and the striker was left with a routine header into the empty net.
Kenny Dalglish introduced Andy Carroll and Jordan Henderson in search of a vital winner as he side look to stay in the hunt for a Champions League football next season.
As the game reached it’s conclusion, the duel between Ruddy and SuÃ¡rez came to the fore.
After 78 minutes, the Uruguay international was able to steal possession from Barnett, but his low shot was tipped wide by Ruddy. The next chance fell to an unmarked Carroll but his headed effort flew past the post.
Liverpoolâ€™s determination to snatch a winner left Jamie Carragher and Srktel exposed to opposition counter-attacks.
A swift Norwich move saw Kyle Naughton deliver a ball into to the box aimed at Holt, but the striker directed his header straight at Reina, who palmed clear.
The final say in an entertaining and open game would fittingly go to Ruddy.
Deep into stoppage time, SuÃ¡rez connected with a cross to push the ball towards the top corner, but the visitors werenâ€™t to be denied a hard-fought point as Ruddy, at full-stretch, pushed the effort over the bar.
Liverpool: JosÃ© Reina, Jamie Carragher, JosÃ© Enrique, Glen Johnson, Martin Skrtel, Steven Gerrard, Stewart Downing (Andy Carroll, 80), Charlie Adam, Dirk Kuyt (Daniel Agger, 91), Craig Bellamy (Jordan Henderson, 69), Luis SuÃ¡rez.
Norwich City: John Ruddy, Kyle Naughton, Marc Tierney, Russell Martin, Leon Barnett, Wes Hoolahan, Bradley Johnson, David Fox, Elliott Bennett (Grant Holt, 57), Anthony Pilkington (Andrew Crofts, 93), Steve Morison.
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