Their fine, flowing first-half football deserved more than the one goal given to them by Saka on the half-hour mark -- Arsenal's 2,000th Premier League strike.
Villa did not have a single shot, on or off target, in the first half, but improved after the break, finally having an effort at goal in the 61st minute when midfielder John McGinn curled just wide.
However, Arsenal remained content to sit on their 1-0 lead until the final whistle, holding on in relative comfort to move on to 54 points, four clear of United in their bid to secure the final Champions League qualification spot.
A second successive defeat for a below-par Villa means they stay ninth.
With United not in Premier League action this weekend, Arsenal had a real chance to cement fourth spot by securing a fifth away league win in a row -- the first time they have been on such a run since May 2015.
Given how many chances they created in the first half, with Emile Smith Rowe, starting his first game in a month, at the heart of everything, they should really have been out of sight by the break.
Striker Alexandre Lacazette was then impeded by his own man -- Smith Rowe again -- as he looked set to score but the pressure did eventually tell as Saka swept home his sixth league goal of the season with his left foot.
Still somehow in the contest, Villa did start to pose a threat after the break, with McGinn's effort causing some jitters in the Gunners' backline, as Ollie Watkins saw another effort clip the outside of the post and roll wide.
That fifth successive away win never looked in doubt, however, with the final whistle greeted with huge celebrations among fans and Arsenal players as they eye a return to the Champions League next term for the first time since 2016-17.