After the Nigeria international's two-goal performance on Sunday, Redknapp said: "He can be the difference between Everton finishing fourth or not, he has certainly given them a good chance.
"Liverpool will always be red-hot favourites to be fourth, I don't ever really look beyond Arsenal, Manchester United, Chelsea and Liverpool for the Champions League spots, but that could change this season.
"Liverpool had a great win at Bolton and they will be stronger as the season goes on, but it is going to be very tight now between the two Merseyside clubs.
"If Everton can get in there, good for them. I would never have envisaged any other club getting in amongst the four I expect to finish at the top."
Redknapp added: "I brought him to Portsmouth because he was a fine striker. He was sold by someone else after I'd left, and when I returned (from Southampton), I'd been left with strikers not fit to clean his boots - great decision that."