Portsmouth 0 Everton 1: Portsmouth's new-look line-up suffered defeat in the Fratton Park mud as Leon Osman's first-half winner gave determined Everton their third Premiership victory in a row.
With both sides struggling at the wrong end of the table, it was David Moyes's side who held firm against a Pompey side which contained four new faces.
Redknapp paid around £7.5million in midweek to recruit Sean Davis, Pedro Mendes and Noe Pamarot from Tottenham but saw two of them booked and the other - Frenchman Pamarot - looking bewildered in central defence.
Pompey were under the cosh early on and did well to survive a quick blitz that should have had an opening goal in the first minute when Osman missed a simple opportunity.
That seemed to give Portsmouth the spark they needed and they dominated the next 25 minutes, but once they went behind they seemed to lose all their authority.
New signing Benjani Mwaruwari struggled leading the hosts' attack and even the introduction of a fifth newcomer, Emmanuel Olisadebe, in the second half could not help their cause.
Everton had not lost at Fratton Park for 49 years and once they were in front again they looked as though they knew that statistic well.
Midfielder Osman, who notched a reply-header in the FA Cup at Millwall last Saturday, made amends for his early miss here with the bravery to get the winner.
Tim Cahill plainly told him to keep his head up after he nodded a perfect cross over the bar with the fans still coming in.
But Cahill could not have had any complaints with the finishing of Osman just after the half hour when he went into to steer home a loose ball off defender Andy O'Brien's shin after James Beattie headed on Joseph Yobo's long ball forward.
Between miss and hit by Osman, Portsmouth showed promised. Lively Lomana LuaLua also twice tested goalkeeper Nigel Martyn with snap shots.
But there were some anxious moments at the back for Pompey in the absence of suspended Dejan Stefanovic and Everton began to sense their opportunity for more relegation relief.
Kevin Kilbane missed two more chances with headers to put them further in front by half-time.
And although they had to survive a scare when referee Andre Marriner failed to spot Yobo tugging on the sleeve of LuaLua, their defending was dedicated after the break.
Despite Pompey's growing pressure they barely created an opening until Olisadebe replaced midfielder Richard Hughes and made a penetrating run that had Martyn diving to save.
However, Everton always seemed intent to hold their lead and protect it.