With fifth-placed Liverpool recording three points against Bolton earlier in the afternoon it was vital Everton continued their excellent form against fellow European hopefuls Pompey.
Everton were one up after less than a minute when Yakubu won a free-kick five yards outside the penalty area.
Steven Pienaar stepped up to float the ball into the box, but what should have been a straightforward clearance for Sol Campbell backfired horribly when he failed to connect with the ball.
An onrushing Yakubu took full advantage as the ball sat up for him to head home his 17th goal of the season with David James in no-man's land.
Yakubu won a near identical free-kick minutes later, but Lee Carsley fired over the bar much to Portsmouth's relief. There was no doubt Everton had been buoyed by the early goal as they set about a rattled Pompey defence.
However, as the game wore on Glen Johnson and Niko Kranjcar began to prove a handful down the right-hand side with a couple of forays into Tim Howard's area.
Everton continued to dominate the half, but a bizarre goal on 38 minutes drew the sides level. Johnson crossed a wicked ball in from the right which was glanced by Jermain Defoe into the back of a bemused Howard's net for an undeserved equaliser.
Harry Redknapp would have known at half-time that the goal could not mask a distinctly below average performance from his side and he would have demanded a lot more creativity in the second 45 minutes.
Whatever Redknapp said had an effect because Portsmouth came out for the second half looking far more composed. Kanu could have put them ahead on 50 minutes, shooting straight at Howard from six yards out under pressure from Joleon Lescott.
The game was looking far more well-matched with both sides threatening on a number of occasions, although all Portsmouth's play was coming from midfield with Defoe and Kanu rarely involved.
It was Moyes who decided to throw caution to the wind though by introducing Andy Johnson for Tony Hibbert with 25 minutes to go.
Everton immediately looked more dangerous with Johnson's pace causing all sorts of problems for Hermann Hreidarsson. The diminutive striker actually had the ball in the net on 69 minutes but Yakubu was fractionally offside when he played Johnson in.
When the inevitable goal did come it was combative midfielder Tim Cahill who rose highest to bury his effort past David James after a wonderful cross by Pienaar who had received the ball after good work from Yakubu on the right side of the penalty area.
Man-of-the match Yakubu wrapped up the victory with a magnificent goal in the 81st minute.
Carsley dispossessed Pompey sub John Utaka and fed the ball to Johnson who, after a short run, hit a long pass over the head of Campbell to Yakubu.
The Nigeria international ran into the area, turned the former Arsenal and Spurs defender, before rifling the ball past James as Johnson attempted to made a last-ditch challenge.