Moyes made four changes to the team which had dismantled Phil Brown's Hull City in mid-week, with Saha, Fellaini, Cahill and Yobo all returning.
A bench including Yakubu, Neill, Hibbert, Jo and Bily highlighted the strength in depth Everton have built even with the likes of Arteta, Jagielka, Neville and Anichebe still out with long term injuries.
Portsmouth, in light of what's happened in the summer, are a patched up team of average to decent players who've been thrown together at the last minute and are going to struggle this season if their opening few games are anything to go by.
But on the evidence of this game alone you'd have to say they aren't nearly as bad as they've been made out. They put the blues under a lot of pressure at times and never stopped working. They look a lot stronger than Hull for example.
Indeed, they nearly took the lead early on when Dindane went through and managed to get a shot in despite pressure from Distin, but Howard was equal to it and palmed the ball away.
At the other end - David James - one big name that Pompey did manage to hold onto this summer, managed to get in the way of a Fellaini header when the Everton midfielder got above the Portsmouth defence and should have scored.
The highlight of a scrappy first half came just before half time, as Saha brought down a 60 yard ball from Heitinga superbly, before going on to lash it into the roof of the net beyond James. It was a superb piece of skill and it's hard to imagine any other Everton striker of recent years having the ability to do that - even The Yak. Brilliant finish and he really looks on top of his game at the moment.
The second half saw Portsmouth almost lay siege to the Everton goal at times. Either that or kick our players up in the air. Pienaar was on the wrong end of a horror tackle and was caught late and high on the inside of his knee. Initially, it looked like he will surely join the list of long term injured but reports today suggest he may only have severe bruising and hopefully won't be out for too long.
He was replaced by Bily who nearly had his head taken off instantly, but luckily escaped with nothing worse than a ripped jersey. He put a few decent crosses in but will need time to get up speed in this sort of game, which is a lot different than a Europa League game or a trip to Hull City reserves. But he certainly looks promising.
With Portsmouth pressing, Leighton Baines cleared an effort off the line and Moyes brought Hibbert on for the dissapointing Osman to tighten up the defence.
Cahill had an effort cleared off the line at the other end but Portsmouth did most of the attacking and Howard made several good saves including one with his shoulder. It was backs to the walls stuff towards the end but the back 5 were excellent and did a great job to keep another clean sheet and secure the 3 points.
The poor start to the season now seems to be behind us and the next two matches - Bate and Stoke City - offer further opportunities to get points onboard and give valuable playing time to players like Yakubu, Bily, Neill and Heitinga.