Lucas Perez gave the Premier League outfit the lead in the first half before Theo Walcott netted his 100th goal for the Gunners after the restart as his team booked a last-eight tie with fellow non-league side Lincoln City.
Sutton had their chances in front of a capacity crowd at their home ground but they were unable to take them as Arsenal eventually eased to victory.
Arsenal went into the match as many as 104 places above their hosts in the English football pyramid, but it took Arsene Wenger's side a while to get going on Sutton's artificial pitch.
They controlled the opening stages but with 16 minutes gone, they had only registered one shot on goal with Mohamed Elneny firing harmlessly over the crossbar.
Sutton began to grow into the match but just before the half-hour mark, Arsenal opened the scoring through Perez who found the bottom corner with a cross which had been intended for Walcott, who failed to get a touch.
Moments later, Walcott sent a shot a couple of yards over the crossbar from distance before Alex Iwobi wasted an opening inside the penalty area, with his shot deflecting off a defender and going wide.
However, in the final minute of the first half, a mistake by David Ospina presented Adam May with a chance to bring his team level but despite advancing into the penalty area, he fired tamely wide from 12 yards.
After the restart, Sutton showed Arsenal that they were not going to wilt away but Arsenal were still able to double their advantage on 55 minutes.
Nacho Monreal advanced into the penalty area and after his low cross was diverted into the path of Walcott by Iwobi, the Gunners skipper converted from close range to reach three figures in an Arsenal shirt.
It appeared that the game was over as a contest but Sutton had other ideas and over the course of the following 10 minutes, they had three chances to halve the deficit.
They came even closer through Roarie Deacon who produced a powerfully-struck shot from 25 yards which beat Ospina, but the winger watched on as his effort struck the crossbar.
Sutton continued to push forward until the final whistle but they could not find the consolation goal that their efforts and overall play deserved, and they will now return to league football in an attempt to remain at the fifth tier of English football.