Liverpool started badly at Villa Park as a poor pass from Adrian -- deputising for Alisson in goal for the visitors after the Brazilian picked up a shoulder injury -- gifted Watkins the opener in the fourth minute.
"It's hard to lose the way we lost tonight. First and foremost well done to Aston Villa, we have to give them the credit they deserve. It was one of those performances where we weren't 100% at it from start to finish," Liverpool defender Virgil van Dijk said after the match.
"Overall, we're all disappointed, we shouldn't have lost with the numbers that we did but it's about sticking together and making sure it doesn't happen again."
If there was an element of good fortunate about Watkins' first goal in a Villa shirt, his second was all his own fine work as he cut inside before firing into the top corner to stun the champions and make it 2-0 in the 22nd minute.
Villa continued to attack after the break and scored a fifth 10 minutes into the second half as Ross Barkley scored his first goal for his new club.
Salah pulled another goal back for the visitors but Villa captain Jack Grealish added another two to seal an historic victory for a club who only avoided relegation from the Premier League last season on the final day of the season.
Villa rained in 18 shots in all on the Liverpool goal and could have added more before the final whistle as they climbed to second in the standings after a third successive win. Liverpool are fifth.
"I think when the first one went in I pinched myself a bit because of how early it was," Watkins said. "I'm delighted to contribute and that we won at the end of the day. It's unbelievable to score and get a hat trick."
The lopsided scoreline also means Liverpool are the first reigning Premier League champions to concede seven in a game in English football's top division since 1953.
Information from Reuters was used in this report.