Daryl Murphy missed a gilt-edged chance for Ipswich in the second half but Grabban could have claimed a hat-trick after lobbing over when clean through and then seeing a shot cleared off the line by Tommy Smith.
Norwich shaded the early possession, but it was typical derby fare played out under a red-hot atmosphere but with little composure.
A nice break from Norwich right-back Steven Whittaker saw his shot comfortably gathered by Gerken with the angle against the defender.
The Town keeper was again equal to a shot from outside the area, from Grabban after good work from Nathan Redmond halfway through a tight first half.
Two minutes later, the visitors broke the deadlock after a horror show from the Town defence.
After a corner was initially cleared, Alex Tettey headed back in and Grabban got in between Skuse and Gerken to head in from close range with the home defence claiming offside.
It was his fourth of the season after scoring twice in midweek against Blackburn, following his first goal for the club against Watford last Saturday.
Ipswich went close to equalising in the 29th minute with David McGoldrick shooting just wide after a neat free-kick from Skuse.
It took Ipswich 37 minutes to finally test John Ruddy, though Murphy's shot lacked power, before they almost equalised five minutes after the restart when a patient build-up lead to Jay Tabb's teasing cross met powerfully by Murphy who headed wide of the far post from the edge of the six-yard box.
Just two minutes later, Norwich were guilty of missing an equally good chance when Javier Garrido's through ball found Grabban in space but he opted to try and chip Gerken and a great chance to provide breathing space sailed harmlessly over the bar.
Shortly before the hour mark, McGoldrick tested Ruddy at his near post before Grabban saw a speculative volley pushed away by Gerken.
The dangerous Norwich striker went even closer after being released by Bradley Johnson but, after rounding Gerken, his effort was cleared off the line by the backtracking Smith.
With neither side giving an inch, Town sub Alex Henshall got beyond the Norwich defence but his dangerous cross was hacked clear by Michael Turner.
With 10 minutes to go, Wes Hoolahan almost made the points safe breaking clear down the left but having a powerful shot blocked by Gerken.
Real chances, and entertainment, was few and far between as the clock ticked down and leaving the Norwich fans celebrating a local derby victory.
- Sports & Recreation
- Dean Gerken
- Daryl Murphy
- Cole Skuse