De Gea made 11 saves in the second half at Wembley as United clung on to Marcus Rashford's first-half strike to win 1-0 -- Solskjaer's sixth win in six matches since taking over following Jose Mourinho's sacking.
At times it appeared to be De Gea versus Tottenham as he made incredible stops to deny Dele Alli, Harry Kane and Toby Alderweireld -- many with his legs.
No other Premier League keeper has made as many saves in 90 minutes as De Gea managed in 45 at Wembley and Solskjaer, who played in United teams with Danish great Peter Schmeichel and Dutchman Edwin van der Saar between the posts, said the 28-year-old could surpass both.
"We had a good back four and David in behind them was unbelievable. You are allowed to have a good goalkeeper.
"I've played with a few fantastic goalkeepers. We have a tradition of having them and he has grown and grown. He deserves that man of the match today."
It was not De Gea's busiest day, though, since he arrived at United from Atletico Madrid in 2011. In 2017 he pulled off 14 stops in a league match at Arsenal.
"I was feeling very well with the first two saves, it was a great game," De Gea said. "I don't even remember some of the saves so I can't pick a best." (Reporting by Martyn Herman, editing by Ed Osmond)
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