Revenge does not form part of Roberto Martínez's vocabulary. He is too urbane, too polite, too magnanimous. Yet the fact remains that, since he left the Liberty Stadium in 2009, a section of the Swansea fans have branded him "El Judas" and City's 3-2 win in May pushed his Wigan side to the relegation trapdoor. Now, in a role reversal, his Everton team beat his former employers by the same scoreline to ensure they remain imperilled.

Swansea may not play like a team in danger of the drop but, after going eight games without a win, their plight grows worse by the week. In contrast, Everton are now on their best run at Goodison Park since 1986, having recorded an eighth successive home victory.

The common denominator has been Martínez, an expert at turning one point into three. Often his input comes in the form of substitutions. On Saturday, his alchemy came in his half-time team talk. "In the last 20 minutes of the first half we were too open," the Everton manager said. "We changed that mentality and focus." Romelu Lukaku and Kevin Mirallas, hitherto ineffective, returned re-energised. Both played pivotal parts in the decisive five-minute spell that yielded two goals.

Everton's second goal amounted to a long-range one-two between the two Belgians. Lukaku laid the ball into Mirallas's path and the winger arced his run around the Swansea defence before crossing for the striker to finish. Destroyer turned decoy for their third as Lukaku missed Mirallas's corner, the ball was allowed to bounce in the six-yard box and Ross Barkley emerged unnoticed to head in what proved the winner.

His marker, it emerged, had been the subject of an unwitting bodycheck by his captain. "He is [José] Cañas's man but he gets blocked off by Ash [Ashley Williams]," Garry Monk, the Swansea manager, said. "If I look at most of the goals that have gone against us in my time, they are mainly individual errors."

His frustration was compounded by the context. "There is always a period when the opposition have pressure and you have to manage it properly and get through it unscathed," he said. "We didn't do it in that five-minute period and it cost us dearly. It gave us too much of a mountain to climb."

They mounted a valiant effort. Wilfried Bony and Pablo Hernández drew fine saves from Tim Howard before Williams headed in the Spaniard's injury-time corner. It made them the first visitors to Goodison to score twice since November and Martínez, typically forgiving past slights, tipped his old club to survive.

"I know for a fact they will get enough points to achieve their aim this season," he insisted. As the instigator of their brand of passing football, his knowledge of City proved useful. "Swansea are one of the best teams in possession in the league and you have to use that to your advantage," he added. So Everton did for the opening goal, catching Swansea on the counterattack, isolating the speedy Barkley against the slower Chico Flores and seeing the Spaniard trip the Englishman. Leighton Baines converted the resulting penalty.

Yet Swansea's leveller had the stamp of Martínez, too, whether with the ability to switch play or in the involvement of an overlapping full-back. Wayne Routledge picked out Àngel Rangel, who had escaped the attentions of a ball-watching Aiden McGeady. The Spaniard centred to give Bony a simple finish.

"I am a bit to blame for how they play," said Martínez. Having taken six points against Swansea this season, he may share a different form of responsibility if Swansea City defy his prediction and slip out of the division.