Rafael Benítez must be starting to sweat. The Liverpool manager has come off second best to David Moyes before in a fight for fourth place, but more troublingly for the Spaniard, the Everton team who finished above their sworn Merseyside rivals four seasons ago were inferior to the present wearers of the blue jersey.

Just like the race for the Barclays Premier League title, the battle to secure the coveted last Champions League berth is fast becoming a test of nerve, but even with Liverpool breathing down their necks, Everton are refusing to flinch.

Liverpool’s grasp on fourth lasted only a few hours yesterday as Everton emerged victorious from another thorough examination to record their fifth successive win and again move three points ahead of Benítez’s team. Yakubu Ayegbeni may have caught the eye with his seventeenth and eighteenth goals of the season — no wonder Harry Redknapp bemoaned Portsmouth’s decision to sell the Nigeria striker — but it was Everton’s sheer force of will that stood out at Goodison Park.

This was always going to be a testing week for Moyes’s men, even ignoring the fact that many of the squad had been laid low by a stomach bug, but they have not only come through it boasting the maximum six points available but, as the manager implied, with an ever greater sense of belief.

Only Chelsea have won more on their travels in the Premier League than Portsmouth this season, but while Redknapp’s team proved more obdurate opposition than Manchester City had last Monday and probably looked the more likely victors in the first period of the second half, Everton are not to be denied at the moment.

The only surprise is that some bookmakers have made Liverpool the odds-on favourites to finish fourth when Everton’s easier run-in and greater consistency augurs so well for them. Chelsea still have to visit Goodison Park, but the Merseyside derby on March 30 is sandwiched between trips to Manchester United and Arsenal for Liverpool that threaten to make or break their season.

“It’s been a big week for us,” Moyes said. “We’ve realised now we can play against any team and cause problems, and even with a bit of sickness about the place, we’ve still been able to get a result. We’ve got a great team spirit.”

Dogged and determined though they were, it was Everton’s plethora of match-winners and a shrewd substitution from Moyes that swung the game in the home team’s favour. With Portsmouth looking dangerous and Everton subdued, Moyes threw on Andrew Johnson and the forward’s impact was tangible, his pace and penetration bringing an added dimension to their play that ultimately paid off when Tim Cahill scored the game’s decisive third goal.

Everton had looked like running away with it when Yakubu headed home after just 55 seconds, when Joseph Yobo flicked on Steven Pienaar’s free kick, but against the run of play, Portsmouth pulled a goal back through Jermain Defoe and grew in confidence thereafter.

Under the watchful eye of Fabio Capello, the England manager, Defoe picked the perfect time to claim his third goal in four matches when he got the faintest of touches to Glen Johnson’s inswinging cross to score, but Portsmouth failed to make their possession and dominance in the early stages of the second half count and when Cahill pounced, the game was as good as over.

Yakubu laid the ball off to Pienaar, who picked out Cahill with a sublime cross. The Australia midfield player, who has barely trained this week through illness, did the rest, hammering a towering header into the corner. Cahill dedicated his tenth goal of the season to Sean, his brother, who was recently jailed for six years for GBH.

When Yakubu added a third, cutting inside Sol Campbell from the left and firing beyond David James after collecting a fine pass from Johnson, Redknapp could have been forgiven for cursing. “I brought him to Portsmouth and when I left they decided to sell him, which was a very clever thing to do,” Redknapp said, sarcastically.

“When I came back I was left with some other strikers who couldn’t clean his boots. I didn’t think he was a £12 million player, that’s why I didn’t bring him back in the summer, but he looks worth the money now.” Everton march on.

Everton (4-4-1-1): T Howard 6 A Hibbert 6 J Yobo 7 P Jagielka 6 J Lescott 6 L Osman 6 P Neville 6 L Carsley 7 S Pienaar Y 8 T Cahill 7 Yakubu 8 Substitutes: A Johnson 7 (for Hibbert, 66min), V Anichebe (for Yakubu, 82), L Baines (for Pienaar, 90). Not used: S Wessels, J Vaughan. Next: Sunderland (a).

Portsmouth (4-4-2): D James 6 G Johnson 7 S Campbell 5 S Distin Y 5 H Hreidarsson 6 P Bouba Diop 4 L Diarra 6 S Muntari 5 N Kranjcar 6 Kanu 5 J Defoe 6 Substitutes: J Utaka (for Bouba Diop, 77min) Not used: J Ashdown, Lauren, M Baros, S Davis Next: Aston Villa (h).