Gomes kept a third successive clean sheet in Saturday's goalless draw against Fulham, producing a string of fine saves as Spurs escaped Craven Cottage with a point.
Redknapp admits to be being mystified by Gomes' reputation as one of the world's finest keepers when he initially assumed control of relegation-mired Spurs in October last year.
On point: Gomes kept Fulham at bay with a string of sublime saves on Saturday
A succession of high-profile blunders had shattered the 28-year-old's confidence and left fans questioning just why the £7.8million signing from PSV Eindhoven was so highly rated.
But Gomes, with the help of goalkeeping coach Tony Parks, has flourished this season and Redknapp now understands the rave reviews.
All smiles: Redknapp is delighted with the form of his goalkeeper Gomes
'There was a time when I had my doubts about Gomes,' said Redknapp. 'When I first arrived at Tottenham I thought 'we've got a problem here' because he was going through a bad time.
'Tony Parks coming has made a big difference. Tony had him working on the training ground while before he was looking at the technical side of it.
'The hard work has got into his head and given him the confidence he needed.
'When Gomes joined Tottenham, Tony Adams said to me that Spurs had signed the best keeper in the world. Tony had been working in Holland.
'Guus Hiddink, who had him at Eindhoven, was saying the same thing.
'I thought are they all right or what? Tony's not drinking any more. But now he looks a terrific keeper.'
Gomes' reflexes kept Tottenham in contention throughout the first of two London derbies in three days, with West Ham next up at White Hart Lane tomorrow.
Fulham created far more chances than Champions League-chasing Spurs and Redknapp believes the outcome - and his satisfaction with a point - illustrates how difficult the Barclays Premier League has become.
But the former Hammers manager remains convinced his team are strong enough to finish in the top four.
'It's a good point at Fulham - they beat Manchester United convincingly last weekend,' he said. 'I thought Chelsea would win, not draw, at Birmingham on Saturday.
'I also thought they'd go to West Ham and win, but it's so difficult at the moment.
Battle ahead: Several teams are challenging Tottenham for a place in the top four
'It's hard to get three points. Anyone can close the gap on Chelsea because they haven't been that convincing but they still have a nice lead.
'Other clubs have improved their squads and are having a go. Every game is more difficult.
'Smaller clubs are no longer rolling over for the bigger ones. It's hard to pick up results.
'But I still think we're good enough to finish in the top four. There won't be much between us and Aston Villa and it will be interesting to see how Manchester City go now.
'I think we've got a chance of breaking into the top four. I've told the players we can do it, let's have a go.'
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