The Crystal Palace youngster, signed from Peterborough over the summer, scored his first goal for the club in the 3-1 victory over Crystal Palace on Saturday Night Football.
The game capped a remarkable rise from non league to top flight for the 22-year-old and Redknapp said that it was a dream day for Gayle, who was allowed to play in his natural position after appearing on the left wing in the first two games of the season.
"I can only imagine how good he feels," said the Sky Sports expert.
"Just over a year ago he was playing in non league for Bishop's Stortford. What a story that is. Now he's mixing with the big boys in the Premier League and scoring winning goals.
"He's 22 years of age and probably dreamed of what has happened today. I thought his all-round play today was really good. He was happy to go past people.
"Ian Holloway spoke about the fee because £6million is a lot of money and that's probably where the pressure's come from, but I think today he showed he can play at this level and not have a problem. He was an absolute nuisance.
"The hardest thing in the world when you're a footballer is not playing in your best position. He's signed for Palace and probably all summer he was thinking he wanted to play up front and be in front of the width of the goal post getting chances.
"Ian Holloway alluded to 'needs must' and at times they've had to play a different system and he's had to play on the left and do a job for the team.
"Today the Palace fans saw the real Dwight Gayle where he can do the most damage and I thought today he was exceptional."
Newspaper headlines claimed Palace boss Ian Holloway was under pressure going into the game and he was visibly thrilled by the victory, dancing along the Selhurst Park touchline at times.
And Redknapp says he is starting to establish an identity on Palace, who bounced back after Steven Fletcher had pulled Sunderland back into the game.
He said: "You want to see a smile on his face because he looks like he's found it difficult in the first two games,
"There is pressure when you go into the Premier League. Everyone has a view now; phone-ins, social media and people putting pressure on you.
"There's people like myself questioning where people are playing. Dwight Gayle in the first couple of games was playing on the left side of midfield, but today you saw him playing closer to Chamakh and already you could see a difference.
"I saw an identity today. They were excellent today. They had to show real character because in the Premier League when a team comes back at you then you have to go again and raise yourself.
"That's exactly what they did."