Villa just about came out on top in the closing stages of a fairly even contest at Villa Park.
Graham Potter's Brighton - who are now without a Premier League win in their last seven - had the better chances in the first half but Leo Trosard and Tariq Lamptey were denied by fine saves from home keeper Martinez.
Brighton controlled the game for large periods and made changes towards the end as Alexis Mac Allister, Neal Maupay and Solly March were introduced as Albion went for the three points.
But it was Villa who exploited the extra space and Watkins and Mings sent Villa Park wild as their goals in front of the Holte End sealed the win on Gerrard's big day.
Potter's team drop down to eighth while Gerrard's Villa - who had lost their previous five - move up to 15th on 13 points from 12 matches.
It's been a hectic two week for Gerrard, who left Rangers to join Villa following the sacking of Dean Smith, but said his focus was always on preparing his team for a tricky first match.
"Graham is an outstanding coach," said Gerrard. "He has a lot of support around him. He has implemented a style that are a real possession based team.
"It was important that we didn't chase lost causes otherwise you are made to pay for that. We wanted to own the middle of the park with or shape and structure.
"We wanted to block the middle of the pitch and when our moments came we wanted to semi-counter and full counter and wanted to hurt the opposition.
"It took until the last 10 or 15 for us to look like a real threat. But we have a lot of attacking players in squad who can run and who are dangerous.
"We allowed them to have the ball in certain areas of the pitch and when Brighton tried to win it from us, we made them pay."