Emiliano Buendia’s header in first half stoppage time separated the sides to leave the Toffees still just five points above the relegation zone in 16th.
Duncan Ferguson took temporary charge of Everton following the sacking of Rafael Benitez last weekend after a run of just one win in 13 league games.
Ferguson was unbeaten in three matches as caretaker boss against Chelsea, Manchester United and Arsenal before Carlo Ancelotti took charge just over two years ago.
But he could not replicate that success as former Liverpool captain Gerrard got one over on his old rivals.
Ferguson bought a round of drinks for fans in a pub next to the stadium before kick-off and got the raucous atmosphere he was looking for.
Both sides flew into tackles, but there were few clear-cut chances in the first half.
Ollie Watkins should have done better when he prodded wide with just Jordan Pickford to beat.
Another former Liverpool midfielder Philippe Coutinho was quiet on his first Villa start since joining on loan from Barcelona, but had a part to play in the only goal.
The Brazilian’s header was tipped over by Pickford.
From the resulting corner, Lucas Digne came back to haunt his former club just weeks after leaving Everton as his corner was flicked in by Buendia.
Digne and Matty Cash were hit by a bottle thrown by the home fans as they celebrated the goal.
Everton should have salvaged at least a point after the break in their battle to beat the drop.
Dominic Calvert-Lewin and Richarlison started together up front for the first time since August and both the Toffees star men were guilty of missing big chances to equalise.
Richarlison headed over before Calvert-Lewin failed to make a good connection to Anthony Gordon’s teasing low cross.
Ben Godfrey’s effort was cleared off the line by Tyrone Mings and Yerry Mina twice should have done better with headed efforts that drifted off target.
But Villa held out to continue Gerrard’s impressive start to his managerial career in the Premier League as they move up to 10th in the table.