Redknapp was in the dugout just four days after being arrested and quizzed by police as part of the football corruption probe.
The veteran former West Ham and Southampton boss was given a hero's welcome by the 20,000 Pompey fans desperate for him to clear his name and continue his bid to lead the crisis hit South Coast team into Europe for the first time.
On the pitch Redknapp endured an afternoon of frustration as Pompey were thwarted by a stubborn Everton defence led by England defender Joleon Lescott and goalkeeper Tim Howard.
Pompey, protecting a club record nine-game unbeaten Premier League run, almost found themselves in front in the 11th minute when powerhouse midfielder Sulley Muntari sliced a shot into the sidenetting.
Croatia midfielder Niko Kranjcar should have scored 15 minutes later when he latched onto Benjani's headed knock down, but blazed a half-volley over and into the stands.
Muntari caused more havoc in the Everton defence six minutes before half-time when his 25-yard free-kick flew just wide off the head of the imperious Lescott.
Howard produced his best save on the stroke of half-time to turn Muntari's long-range free-kick one-handed onto the crossbar.
Pompey continued to dominate in the second half and Pedro Mendes almost lived up to his 'rocket man' nickname when he smashed a dipping volley inches over.
Kranjcar, England's tormentor in chief at Wembley last month, missed another gilt-edged chance in the 49th minute when he toe-poked wide from six yards after Glen Johnson had burst free and crossed from the right.
Everton, themselves unbeaten in seven, failed to score for only the fourth time this season but gave David James his easiest afternoon of the season with just one shot on target.