The Championship side took a surprise lead in the 25th minute when Fred Onyedinma popped up in the perfect spot in front of goal and side-footed past Joe Hart to make it 1-0.
Uche Ikpeazu rolled Toby Alderweireld and his cut back deflected off Tottenham defender Davinson Sanchez and fell invitingly for Onyedinma to fire low past Hart.
However, Spurs hit back in first-half stoppage time as Gareth Bale turned in a clever shot from close range from a Lucas Moura through ball to level the score before the break.
With passage to the fifth round looking in doubt, Tottenham manager Jose Mourinho brought on Pierre-Emile Hojberg at half-time and Harry Kane shortly before the hour, but the hosts continued to provide stiff resistance as the match stayed deadlocked at 1-1.
“If it goes to extra time, it would be bad for both teams,” a relieved Mourinho said. “The attitude from the players from the first minute was excellent, then the players on the bench, they came with the intention of giving something to the team, so overall it was a good squad performance.”
Back-to-back goals from Harry Winks and Tanguy Ndombele finally broke Wycombe’s resistance as Tottenham pulled away and moved into the last-16 of England’s oldest cup competition.
Spurs added a fourth as full-time approached when Ndombele’s shot from close range took a deflection and found its way into the back of the net.
“The scoreline is probably not a reflection of the game although they were fantastic at the end — I am flattered they had to put some big names on to get in front,” said Wycombe boss Gareth Ainsworth.
“We looked tired. We’ve given everything and there’s no disgrace from our boys. We’ll take a lot of heart from this.” Next up for Tottenham in the FA Cup is a fifth-round match against Everton at Goodison Park.