Defender Ramiro Funes Mori also added to the Spaniard's woes ahead of Saturday's FA Cup semi-final against Manchester United with this fixture's 21st red card in the last 47 Premier League encounters.
That was compounded by fellow centre-back John Stones limping off injured after the third goal went in. That was Daniel Sturridge's 50th goal for the club and followed two headers from Divock Origi and Mamadou Sakho just before half-time.
Philippe Coutinho's 76th-minute strike sent visiting fans heading for the exits and every 'Ole' which rang around Anfield towards the end was a dagger to the heart of Martinez and those who remained in the away end.
Sturridge, only on because Origi was carried off on a stretcher with a serious-looking ankle injury as a result of Funes Mori's stamp, became the fourth-fastest Liverpool player to his half-century by reaching the landmark in just his 87th match.
The England international's current strike-rate is better than that of Luis Suarez (91 games), John Aldridge (92), Michael Owen (93), Robbie Fowler (94), Kenny Dalglish (99) and Ian St John (111) - impressive considering the amount of time he has lost through numerous injuries.
By contrast Everton's premier striker Romelu Lukaku, included in Martinez's strongest possible line-up despite a looming Wembley date, barely had a sniff all night.
For 25 minutes Martinez's boldness appeared to be paying off but familiar weaknesses were soon exposed.
The visitors, whose longest winless run at Anfield was extended to 16 matches, were initially brighter and quicker to the ball, but unlike Borussia Dortmund a week ago they failed to take advantage of their early pressure.
Kevin Mirallas twice missed the target from good openings before Lukaku was denied by Sakho at full stretch.
Liverpool's best player during Everton's period of dominance, Adam Lallana, could curiously have had a hat-trick in the first half-hour, squandering the best chance as early as the sixth minute when he sprung the offside trap but shot straight at Joel Robles.
Everton's Gareth Barry, equalling David James' record of 571 Premier League starts, and James McCarthy appeared to have control of midfield but gradually that was wrested from them as Liverpool's relentless attacking started to take its toll.
Coutinho, who gave makeshift right-back Bryan Oviedo numerous problems, had two efforts from long distance while Brazilian compatriot Roberto Firmino was denied by Robles.
Everton's resistance finally gave way a minute before the break when Milner's hanging cross from the right to the far post saw Origi out-jump John Stones to head in his fifth goal in as many games, off his shoulder.
The Toffees' weakness has been to concede goals quickly, verging on a collapse at times, and this was exploited as Milner, this time from the left, exchanged passes with Lallana before crossing for Sakho, criminally unmarked, to power home the header.
Just when Martinez thought it could not get any worse after the break, along came Funes Mori's stamp on Origi. It resulted in the striker being carried off on a stretcher holding his head in his hands - which was also Klopp's reaction - and rightly meant the Everton man was dismissed.
The sight of the Argentina international kissing the badge on his shirt as he walked off was somewhat crass, especially with him now weakening Everton's defensive options even further for the semi-final.
Sturridge clinically dispatched Lucas Leiva's pass for the third on the hour before Stones' departure - which left midfielders McCarthy and Muhamed Besic in central defence - and Coutinho's smart finish compounded Everton's misery, a feeling experienced at Anfield all too often since 1999.