Gabriel Jesus slotting home after just eight minutes giving the hosts a 5-0 aggregate lead.
Son Heung-Min celebrates scoring for Tottenham Hotspur.
City advanced 5-2 on aggregate and became the second English team through to the quarterfinals, after Liverpool from Tuesday.
"We have four excellent central defenders". It was his first goal in his last 14 appearances. "The press officer informed me 15 minutes ago Mike Riley was here", he said.
"You create passes to create opportunities but only to pass for itself, that isn't football". The loss still came as a surprise particularly after Brazil striker Gabriel Jesus put the home side ahead in the eighth minute on his first start in 2018. "We are new in that position, so we are so happy for that", said Guardiola. "I cried many times". Yet concentration was lacking when moments later David Silva's attempted crossfield ball to Sané was given away and City were turned. What else is there to do on a Wednesday night?
So bravo Bravo! And bravo the Basel fans.
The loss also ended City's 13-match unbeaten run at home in the UEFA Champions League.
"We have a certain pride", Basel coach Raphael Wicky said, "and against a team that plays every three days and is beating everyone, it's very special".
Spurs held Juventus to a 2-2 draw in Italy in the first leg. The two teams then traded attacks and counter attacks for the rest of the half, but no goals were scored.
Hardly likely tonight. But stick with us to find out.
It was Jesus' first start since the game at Crystal Palace in December, where he picked up the knee injury which had him visibly worried in the immediate aftermath, fearing his season was over and his World Cup debut as Brazil's No 9 was in serious doubt. I'm not going to say we're not going to win. A feature of City's outstanding season has been the flying wing play of Leroy Sané.
So much of this last-16 match-up hinged on brief passages of play.
Before Tottenham could regroup it was trailing, with Higuain the creator.
Another rout seemed in store despite the absence of key Manchester City stars, but the game took an unexpected turn when Basel scored in the 17th minute. Guardiola grew visibly frustrated on the touchline as his side also started the second period slowly.
"It was good", Guardiola said of Foden's appearance.
Guardiola did not want to predict how far his team might be able to go in the competition. Within ten minutes, though, the scores were level: Mohammed Elyounoussi latching onto Blas Riveros's ball into the box and finding himself curiously unmarked.