The goalkeeper, who missed out on a desired move to Manchester United, saved from Jack Grealish and Michael Keane to thwart the Toffees at the Hill Dickinson Stadium.
Unai Emery’s Villa are still looking for their first goal and win of the season and rarely looked like making the breakthrough on Merseyside.
But they at least left with something to show for their defensive effort, thanks to Martinez.
**Analysis**
The World Cup winner had been left out for Villa’s previous match, a 3-0 defeat to Crystal Palace, because boss Emery believed he was not fully focused after United rekindled their interest in signing him late in the window.
But the decision to recall him immediately after no move materialised proved the right one, as his saves ensured Villa avoided a third straight defeat.
His first big stop, from Grealish, was impressive as the shot had taken a deflection off Tyrone Mings.
Yet his second huge save was even better, Keane’s header appearing destined for the net before the keeper brilliantly tipped it over the bar.
Villa also withstood a series of late corners as they held out for a point and there could be no doubting the commitment of Emery’s team.
The concern is their lack of attacking spark. It is now four matches without a goal and they are still searching for their first victory.
Emery’s comments about Martinez on Friday, in which he insisted on the goalkeeper’s commitment to the cause, made the latter’s inclusion no surprise.
The selection of Lamare Bogarde, for just his fifth Premier League start, hadn’t been expected. Emi Buendia was also handed a first league start since May, 2023 with all three of Villa’s new signings on the bench.
It was a selection which suggested Emery wanted to keep things tight but within two minutes Villa should have been behind.
Grealish won the ball in midfield, released Iliman Ndiaye down the right and when he crossed, Beto appeared to have a simple finish only to fire the shot into his standing leg, the ball spinning wide of the target.
That set the tone for the opening spell which saw Villa struggle to get out of their own half.
Martinez saved from Beto at close range, albeit before the offside flag was raised. The keeper then produced an excellent stop with his legs to deny Grealish, whose shot which took a deflection off Mings would have counted.
Villa got a bit better as the half went on but their attacking play remained as sluggish as in the season’s opening matches.
Everton continued to look the more threatening, Keane heading over at a corner, with another then bouncing off the knee and wide of goal.
The visitors had another let-off early in the second half when Beto somehow failed to make contact with James Garner’s inviting cross.
Then, finally, it was Villa’s turn to seriously threaten. Buendia picked up the ball in space, ran at the visiting defence and saw his shot deflect off James Tarkowski and just wide of goal.
Emery’s team were better but it was the hosts who then went close again, Martinez spilling Dewsbury-Hall’s cross and then pushing the ball away from the advancing Ndiaye before Jake O’Brien saw a drive blocked behind.
It was a shaky moment from the keeper but he then reminded everyone of his class with a superb save to deny Keane. The defender’s glancing header, from Grealish’s cross, was heading under the bar before Martinez thrust out a hand to send it over.
Everton pushed for a winner and a mistake from Ezri Konsa saw substitute Thierno Barry race clear, only for Mings to make an excellent sliding challenge to deflect his effort wide.
**Teams**
Everton (4-2-3-1): Pickford, O’Brien, Tarkowski, Keane, Garner, Gueye, Iroegbunam (Rohl 66), Ndiaye, Dewsbury-Hall, Grealish, Beto (Barry 75) Subs not used: Patterson, McNeil, Dibling, Coleman, Alcaraz, Aznou, Travers (gk).
Villa (4-2-3-1): Martinez, Cash, Konsa, Mings, Digne, Bogarde (Lindelof 82), Tielemans (Guessand HT), McGinn, Buendia (Elliott 71), Rogers, Watkins (Malen 82) Subs not used: Torres, Sancho, Maatsen, Proctor (gk), Bizot (gk).