Grant Holt headed the equaliser and then Anthony Pilkington's deflected shot put Norwich ahead.
Canaries skipper Grant Holt equalised two minutes later with a simple finish after Iain Turner had parried a shot from Andrew Surnam.
In Grant Holt, Chris Martin and Wes Hoolahan, they have got three players who are just scoring goals for fun.
Town's 26-goal top scorer Grant Holt struck twice in the last 11 minutes at the Priestfield to rescue a point.
Lambert used 21 different players at Victoria Road, with notable absentees being the injured Grant Holt, Steven Smith and Stephen Hughes.
Meanwhile striker Grant Holt has been told to rest for the next few days, to ease aching after an ankle operation.
But Norwich looked to have rescued a point seven minutes from time when Grant Holt fired home after his turn out-witted Rio Ferdinand.
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Having scored in both Town's opening two games this season, Hibbert has helped make light of the summer departure of 27-goal Grant Holt.
Norwich equalised on 65 minutes when captain Grant Holt converted Wes Hoolahan's cross but the joy was short-lived as Burnley got the late goal.
Promotion-chasing Norwich won praise from their fans at the club's AGM on Tuesday night for not selling the likes of Wes Hoolahan and Grant Holt.
"So many times this season we've thanked Grant Holt, " said Simpson.
Norwich's best chance fell to last season's top scorer Grant Holt, but his header from eight yards floated over when he should have hit the target.
Grant Holt's goals for the champions Norwich got them up but it is a close call whether he or Southampton's Ricky Lambert was the best striker at that level.
Norwich continued to threaten and the hosts felt aggravated for not being awarded a penalty when Cardiff full-back Paul Quinn brought down Norwich striker Grant Holt in the penalty area.
Doherty started the season as club captain under previous manager Bryan Gunn but Lambert has not picked the centre-back for either of his first two league games in charge, handing the armband to Grant Holt.
The Cumbrians have been seeking a target-man to support their attacking options since the departure of Joe Garner to Nottingham Forest in July 2008, and had failed in attempts to sign players such as Grant Holt and Glenn Murray.
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