A stoppage-time penalty by Grant Holt denied Blackburn as Norwich fought back to secure a dramatic point.
Junior Hoilett's 20-yard finish put Rovers ahead before Steve Morison's stunning strike drew Norwich level.
Yakubu took advantage of John Ruddy's error to put the visitors back in front, with Chris Samba's header stretching their advantage.
Bradley Johnson's heavily deflected shot got Norwich back in it, with Holt levelling after Steven Nzonzi handled.
It was a dramatic finish to an absorbing, fast-paced game but Blackburn will be deeply unhappy with referee Anthony Taylor as the decision to award a penalty against Nzonzi was harsh.
Rovers had thoroughly deserved their half-time lead following a first half in which both teams carved out numerous chances.
Kean bemoans penalty decision
The visitors had not managed an away win in the top flight since the final day of last season, but Mauro Formica set the tone in the second minute with a rasping 25-yard drive which flew narrowly wide.
Blackburn's cause was not helped when Morten Gamst Pedersen and Gael Givet collided going for the same ball, both players emerging bloodied and dazed but otherwise unharmed.
It was only after Yakubu sliced another chance into the side netting, a bad miss by the former Everton striker, that Norwich came to life.
BLACKBURN'S AWAY RESULTS THIS SEASON
v Aston Villa 1-3
v Fulham 1-1
v Newcastle 1-3
v QPR 1-1
v Norwich 3-3
Paul Robinson produced a spectacular full-stretch stop to deny David Fox his first goal of the season from 25 yards, before Elliott Bennett fired into the side netting when he should have done much better from eight yards.
It proved a big miss for the Canaries as Blackburn's Hoilett produced a sublime finish into the top corner of the net from 20 yards after evading a couple of challenges in first-half stoppage time.
Norwich were back on level terms through an equally stunning finish by Morison in the 53rd minute, the former Millwall player letting fly from the edge of the area after being played in by Leon Barnett.
But Blackburn looked to have sealed victory with two goals in as many minutes.
Ruddy, who was the hero when his team drew 1-1 at Liverpool last week, gifted Yakubu his third goal since joining from Everton after allowing the Nigerian's shot to creep in at the near post.
Norwich character pleases Lambert
Blackburn's fans were still celebrating that goal when Samba established a two-goal cushion for his side after taking advantage of some poor Norwich marking to nod home Pedersen's free-kick from close range.
When Johnson's 83rd-minute effort defelected in off Jason Lowe it looked like nothing more than a consolation before the referee pointed to the penalty spot deep into stoppage time after Nzonzi was adjudged to have handled.
Blackburn's players strongly appealed but substitute Holt kept his composure to earn the hosts a dramatic point.
Norwich boss Paul Lambert:
"The character my players showed was terrific. I'm delighted with the desire they showed not to be beaten.
"Obviously I'm not happy with the goals we conceded, particularly the two goals in the second half. But as for their penalty, I didn't really see it.
"I also haven't seen on the video yet but the referee has called it and he's made the decision.
"We've had a lot of decisions go against us this season. It's definitely a point gained."
Blackburn manager Steve Kean:
"I feel as though three points have been grasped away from us.
"I asked the referee about the penalty and he told me that Steven had handled the ball. But I've seen it 10 times now and he only had his arms up because he was appealing for a free-kick.
"If the referee sees it again then I'm sure he will admit he was wrong to award it.
"We've just got to keep going. It's tough but we've got to move on."
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