Luis Garcia and John Arne Riise struck second-half goals to send Liverpool fifth in the Premiership.
Garcia lobbed Norwich goalkeeper Robert Green from Riise's pass to open the scoring after 57 minutes.
And Riise was on target seven minutes later after Green saved from Florent Sinama Pongolle, who charged down Craig Fleming's poor clearance.
Ryan Jarvis pulled a goal back with a spectacular 20-yard effort, but Liverpool survived for a crucial win.
The opening 45 minutes was short on quality and chances - with defences taking command.
Doherty had a half-chance for Norwich City after 15 minutes, but he headed Phil Mulryne's free-kick tamely over the top.
Liverpool's attacking options were restricted, and they rarely threatened.
Riise dragged a close-range shot wide, while captain Gerrard was off target with an ambitious effort from 25 yards.
Norwich's best attacking outlet was Darren Huckerby, who was giving Steve Finnan a torrid time.
And it was no surprise when the Republic of Ireland defender was finally cautioned by referee Howard Webb for the latest in a succession of fouls after 52 minutes.
Liverpool sprung a classic counter-attack to take the lead after 57 minutes.
Norwich were almost gifted the lead at one end as Liverpool's defenders were involved in a mix-up.
But within seconds they had swept to the other end, and when Riise's pass found Garcia, he lofted a clever finish over the on-rushing goalkeeper Green.
And seven minutes later Liverpool doubled their lead as Norwich once again pressed the self-destruct button.
Fleming carelessly struck a clearance against substitute Pongolle, and when Green saved his shot superbly, Riise was on hand to score with ease.
Substitute Jarvis gave Norwich hope with a minute left, cutting inside to send a spectacular drive high past Jerzy Dudek from the edge of the area.
Norwich: Green, Helveg, Doherty, Fleming, Charlton, Jonson, Bentley, Mulryne (Brennan 67), Francis (Jarvis 78), Huckerby, McKenzie (Crow 67).
Subs Not Used: Drury, Gallacher.
Booked: Francis, Bentley.
Goals: Jarvis 88.
Liverpool: Dudek, Finnan, Carragher, Hyypia, Riise (Traore 82), Nunez (Hamann 77), Diao, Gerrard, Warnock, Luis Garcia, Mellor (Sinama Pongolle 61).
Subs Not Used: Raven, Harrison.
Booked: Finnan, Hyypia, Warnock.
Goals: Luis Garcia 58, Riise 64.
Ref: H Webb (S Yorkshire).