Gibbs got the ball rolling for Arsene Wenger's side with the opening goal on 16 minutes before Theo Walcott added a second when he slipped the ball beyond bamboozled visiting goalkeeper Shay Given - who was badly at fault for the opening goal - to hand his side a 2-0 lead on 25 minutes.
Spanish midfielder Mikel Arteta rounded off a comfortable win for Arsenal when he smacked a delicious free kick beyond Given from over 25 yards out deep into injury time.
It was a stunning effort and ensured Arsenal had recorded seven successive wins for the first time since October 2007.
This was also the first time since October 1997 that more than one English player had scored for Arsenal in one Premier League match.
Ian Wright, David Platt and Ray Parlour scored back then in a 5-0 win over Barnsley, but this was every bit as comprehensive with Villa finishing the match a distant second in this particular two-horse race.
With London rivals Chelsea and Tottenham drawing 0-0 earlier in the day, Arsenal are now looking good to claim third place in the table and an automatic qualification place in next season's Champions League group stages.
They are three points ahead of Spurs and eight clear of fifth-placed Chelsea, who are in danger of missing out on Europe's premier competition next term despite reaching the last eight of this season's tournament.
Marc Albrighton hammered a shot over the bar for the visitors on six minutes before their day gradually went downhill as Arsenal assumed control.
Given somehow let Gibbs's drive squirm under him and into the net to hand the home side the lead, but the second goal was a thing of real beauty as Walcott took one touch to control Alex Song's long ball before sliding the ball beyond the stranded Given with his second.
Stephen Warnock brilliantly nudged Robin van Persie's shot off his line after Given and Alan Hutton got in a tangle with Arsenal threatening to increase their cushion every time they bounded up the park.
Given atoned for his earlier error by swatting an Arteta drive over his bar while he had to stand tall to repel a shot by Tomas Rosicky in the second period, but the three points were already destined to remain with Arsenal long before that stage.