Leon Osman's first-half goal gave Everton a valuable victory over Harry Redknapp's revamped Portsmouth side.
The home team featured four new signings, but it was the same old story as Pompey failed to pose a threat in the final third of the park.
Osman should have scored with a header before he bundled a close-range effort past Jamie Ashdown after 31 minutes.
New boy Sean Davis had Portsmouth's best chance on 65 minutes, but he shot wildly over the bar from 12 yards.
Pompey had four players making their debut - with former Spurs trio Davis, Pedro Mendes and Noe Pamarot starting and Benjani Mwaruwari also in the starting-line up.
And they were still getting to know each other as Everton wasted a glorious chance to take the lead inside the first minute.
Tim Cahill crossed and Osman arrived totally unmarked at the far post, only to head wastefully off target.
Pompey's new-look strike force of Benjani and Lomana LuaLua was showing some signs of promise, and the latter had a powerful early shot comfortably saved by Nigel Martyn.
But Everton were very comfortable and took the lead after 31 minutes - a scrappy affair in keeping with the quality of the game.
Joseph Yobo's free-kick was flicked on by Kevin Kilbane, and Osman bundled home in a goalmouth scramble, although Portsmouth defender Andy O'Brien may also have got a touch.
Cahill almost added to Everton's advantage with two headers before half-time, but a below-par Pompey side survived.
Portsmouth needed to improve after the break, but Richard Hughes almost gifted Everton a second right after the re-start when he was grateful to see a clearance fly narrowly over his own bar.
Osman then fired only inches wide from 20 yards as Everton threatened to increase their lead.
Portsmouth had barely created an opportunity worthy of the name, but Davis wasted the chance of a debut goal after 65 minutes when he shot over the top from 12 yards.
Portsmouth manager Harry Redknapp:
"I thought we started well, but Everton set their stall out to play a certain way and when they get ahead they make it very difficult.
"We needed to bring new players in. We could either have a go or sit there and do nothing and just get relegated - we've had a go and the players I've brought in will be outstanding for this club.
"I felt we needed eight players to be honest and that's no exaggeration. We will keep looking around because I still think there are one or two holes we need to fill."
Everton manager David Moyes:
"The players put in a real big shift here in difficult conditions, but I thought Joseph Yobo was top man for us - his defensive performance was just outstanding.
"We have won three Premier League games in a row now, and I think the players deserve a lot of credit for bouncing back the way they did after losing the derby at home to Liverpool.
"The pitch wasn't very good and it didn't make for a great Premiership match, but coming to Pompey and winning is a big result for us."
Portsmouth: Ashdown, Griffin, Pamarot, O'Brien, Taylor, O'Neil, Pedro Mendes (Diao 73), Davis (Karadas 87), Hughes (Olisadebe 61), LuaLua, Mwaruwari.
Subs Not Used: Westerveld, Priske.
Booked: Pedro Mendes, Davis.
Everton: Martyn, Hibbert, Yobo, Ferrari, Nuno Valente, Arteta (Bent 90), Cahill, Neville, Osman, Kilbane, Beattie (Weir 88).
Subs Not Used: Wright, Davies, McFadden.
Booked: Ferrari, Kilbane.
Goals: Osman 31.
Ref: A Marriner (W Midlands).