Arsenal went into the Premier League fixture looking to move back to the top of the standings and having had two days extra rest than Villa, who competed in the Europa Conference League on Thursday.
Mikel Arteta also selected his strongest lineup, rather than rest players ahead of the second leg of their Champions League quarter-final against Bayern Munich on Wednesday.
However, the Gunners were unable to make the breakthrough against the West Midlands outfit, who held firm in the first half before coming on strong after the break.
With six minutes remaining, substitute Leon Bailey coolly converted at the back post to put Villa ahead, before Watkins broke clear from the halfway line three minutes later and produced a deft finish into the far corner.
In doing so, Watkins scored his 19th Premier League goal of the season, equalling Christian Benteke's total in the 2012-13 campaign as the most ever by a Villa player in the division.
What did Watkins have to say?
While the 28-year-old was quick to heap praise on his team, the England international felt that Villa's opponents contributed to their own downfall, showing signs of fatigue in the latter stages.
Speaking to Match Of The Day, Watkins said: "I felt like we grew into the game a lot. The longer Arsenal didn't create much, we could see from their body language that they were getting tired and definitely getting frustrated and I think we used that as momentum and motivation really.
"We grew into the game and we played some really good football. We didn't go long too much, the boss demanded that we played out and were brave. If we lost the ball and they scored from it, so be it, but that's the game plan and it worked today. We frustrated them and in both boxes, we were really good.
"When I saw Youri (Tielemans)'s hit the bar and the post, I thought 'ah no, it's not going to be our day is it?' I was always calm that we were going to get something. We were frustrating them, we were creating lots of chances and we could see that they were getting tired and we kept plugging away and we stuck at it.
"I'm delighted with that, it's a massive win. A lot of people doubted us or definitely favoured Arsenal coming into this game. We've been playing well and been a bit lackadaisical and lost concentration, so today, we showed we're a really strong team and we're fighting for the Champions League."
Where does win at Emirates leave Villa?
As well as the ramifications that Villa's win has for Arsenal's title hopes, Unai Emery's side completing the double over his former club has significantly boosted their hopes of qualifying for the Champions League.
Villa now sit three points clear of Tottenham Hotspur in the race for fourth position, albeit having played one game more than the North Londoners.
Before returning to league action against Bournemouth on April 21, Villa make the trip to France to face Lille in the second leg of their Europa Conference League quarter-final, holding a 2-1 lead.