Blackpool made the more positive of the starts as Tony McMahon drilled towards the bottom corner early on, before Francois Zoko saw his header somehow kept out of the top corner following a six-yard attempt.
The visitors tried to force an opener just before the break, but Grabban could only drag his effort wide of the post from distance.
The game burst into life early in the second half as Blackpool grabbed the lead after only a minute when Nathan Delfouneso lashed a shot into the top right corner.
Their advantage was not to last too long however, as City replied with a goal of their own, but it was courtesy of a Blackpool player as Donervon Daniels put into his own net to level things up at 1-1.
The hosts sought to push back in front and they almost found a vital goal through Joan Oriol, whose long-distance shot was saved in the top left corner.
The visitors stole their victory with 10 minutes left to play as striker Grabban was picked out by Johnson, leaving the frontman to convert into the top corner to make it 2-1.
The Canaries then secured top spot when Murphy tucked home from close range after being picked out Cameron Jerome.