Harry Redknapp could not end a troubled week with a victory as Everton frustrated his Portsmouth side in a drab game at rain-soaked Fratton Park.
Portsmouth's Sulley Muntari (left) went close with two free-kicks
Portsmouth had the better of the chances, with Sulley Muntari twice going close with free-kicks.
Pedro Mendes and Niko Kranjcar were also narrowly off target, but Pompey found Everton in defiant mood.
Leon Osman had Everton's best opening after the break, but failed to control with only keeper David James to beat.
Portsmouth boss Redknapp has protested his innocence since being one of five men arrested on Thursday on suspicion of conspiracy to defraud and false accounting, and he would have been relieved to get back to football at Fratton Park.
Everton, understandably, named the same side that thrashed Sunderland 7-1, but they showed little of that sparkle in the opening period.
Portsmouth almost broke the deadlock, courtesy of those two Muntari free-kicks, but the first was deflected inches wide by Tim Howard's foot and another turned over the top by the Everton keeper.
Everton were struggling to exert any authority in midfield, and Steven Pienaar was booked after a succession of fouls - indeed he was lucky not to be shown the red card for persistent fouling.
Tim Cahill was also shown a yellow card by referee Peter Walton for a crude challenge on Papa Bouba Diop as Everton became frustrated at their failure to find any rhythm going forward.
Portsmouth continued to dominate after the break, with Mendes shooting just over the top and Kranjcar coming closest of all when he narrowly failed to turn in Glen Johnson's cross.
Everton boss David Moyes needed to inject some threat into his side, and he decided to send on Andrew Johnson for Pienaar after 52 minutes.
Osman then missed Everton's best chance when he failed to control Yakubu's header with only James between him and the opening goal.
Everton forced James into his first serious save after 66 minutes, Mikel Arteta curling in a 25-yard free-kick which the England goalkeeper held comfortably.
Portsmouth almost snatched it with five minutes to go when Howard palmed out Diop's shot, but Joleon Lescott's tackle halted substitute Kanu as he attempted to pounce on the loose ball.
Portsmouth manager Harry Redknapp:
"It was a tough game against a very good side. They have two really powerful central defenders in Joseph Yobo and Joleon Lescott and they are very quick on the break.
"But that's 10 games unbeaten in the league for us and that is a fantastic run. We are winning away and finding it more difficult at home, but it's another clean sheet and I've got to be happy with that."
Everton manager David Moyes:
"It was a game where defences were on top. I thought our keeper Tim Howard and the two central defenders Joseph Yobo and Joleon Lescott were fantastic.
"We had to show another side to our game after scoring seven against Sunderland last week and we did that. We kept a clean sheet, which is something I have been going on to them about.
"Portsmouth are a good side so we are pleased to come away with a point."
Portsmouth: James, Johnson, Campbell, Distin, Pamarot, Utaka (Kanu 57), Diop, Pedro Mendes, Muntari, Kranjcar, Mwaruwari.
Subs Not Used: Ashdown, Hreidarsson, Nugent, Taylor.
Everton: Howard, Neville, Yobo, Lescott, Nuno Valente, Arteta, Osman, Carsley, Cahill, Pienaar (Johnson 53), Yakubu (Anichebe 67).
Subs Not Used: Wessels, Hibbert, Jagielka.
Booked: Pienaar, Cahill.
Ref: Peter Walton (Northamptonshire).