But Steve Kean's side will be wondering how they did not pick up a vital three points as they seemed to be cruising to victory with seven minutes left when they led 3-1.
But Bradley Johnson's deflected effort and substitute Grant Holt's stoppage-time spot-kick after Steven N'Zonzi was ruled to have handled the ball, ensured the Canaries rescued a precious point from the match.
The first 45 minutes looked set to be goalless until a superb individual goal by the outstanding Junior Hoilett on the stroke of half time broke the deadlock.
It was a surprising goal for the Canaries to concede as, after Rovers had played well in the opening 15 minutes, Paul Lambert's side had dominated the rest of the first period.
Norwich drew level in the 54th minute with another fine goal, this time Steve Morison beating Paul Robinson with a sweet right-footed volley.
However, Rovers took control of the encounter with two goals in two minutes. In the 63rd minute, Yakubu's low shot beat John Ruddy at his near post, when the Canaries shot-stopper should have done much better.
Almost immediately Chris Samba headed Morten Gamst Pedersen's free-kick past the hapless Ruddy and the points seemed to be heading back to east Lancashire.
But with seven minutes left, Robinson watched Johnson's deflected effort loop over him and, despite Rovers creating the better chances in the closing stages, it was Norwich that drew level thanks to substitute Holt's controversial last-gasp penalty.