Neither side could muster a serious shooting chance in a quiet start to the match, with the first attempt arriving via the boot of Alex Iwobi 20 minutes in for an Arsenal side showing 11 changes from last time out.
Murphy then went close on two occasions but saw his header then shot thwarted by Macey in a matter of minutes.
Another opening came and went for Walcott early on in extra time, but Nketiah had less trouble with his finishing as he nodded the ball past Gunn from a left-sided corner.
Nivea faces backlash for racist ad for 'lighter skin'
Others have pointed out that if the demand was not there for skin-lightening products , Nivea would not be selling them. The campaign and the cream have caused outrage since their debuts, prompting a #TakeItDown campaign on social media.
The Portugal global raced towards goal only to be halted by a Mohamed Elneny foul which could easily have seen the Arsenal man dismissed, with referee Andy Madley lenient in his issuing of a yellow card.
Vrancic then inexplicably fired wide from close range after taking two Arsenal defenders out of the game with a fine dummy.
Arsenal have named their starting side and substitutes to play host to Championship outfit Norwich City in an EFL Cup fourth round tie at the Emirates Stadium this evening.
Nketiah scored with his first touch after 85 minutes, before heading home in extra-time, after 96 minutes, to take Arsenal through.
The Norwich players surrounded referee Madley after he turned own their penalty claims as James Husband and Mathieu Debuchy came together in the box.