The Scotsman stepped in following the sacking of Rafael Benitez but the move did not produce the desired response as Emiliano Buendia’s header in first-half added time settled a scrappy encounter.
Villa’s victory was particularly sweet for former Liverpool captain Steven Gerrard as well as ex-Everton defender Lucas Digne, who provided the corner for Buendia’s winner.
The goal was followed by disgraceful scenes as celebrating Villa players were struck by objects thrown from the crowd.
Everton will feel their second-half pressure, based on an aerial bombardment, should have brought some reward as Dominic Calvert-Lewin turned Anthony Gordon’s cross over from close range and Ben Godfrey’s header was scrambled off the line by a combination of Tyrone Mings and keeper Emiliano Martinez.
It leaves Everton with only six points from their last 42, searching for a new manager, and sitting uncomfortably close to the relegation zone of the Premier League.