Sergio Aguero was typically sublime, but the evening belonged to Gundogan, who contributed 50% of the goals and a large proportion of City's excellent build-up play.
City have stumbled many times in this competiton in the last decade, but all signs suggest they can live up to their potential this year.
Should Guardiola's men beat League One side Wigan Athletic on Monday, they will face an FA Cup quarter-final on the weekend of March 17 and 18. We were clinical and I am delighted with the performance.
Halfway through the Round of 16, the Premier League is looking good for three quarter-finalis ts.
The Spaniard heaped praise on Gundogan and his midfield team-mates, including David Silva who made a return off the bench after injury.
For the last few seasons, we numbered English sides among the poor teams but the impact of a vast amount of money spent on the best managers in the world and some of the most exciting players on the planet in the last 12 months is now obvious.
"With De Bruyne and David Silva, we have a fantastic midfield trio".
It was 24-year-old Kane's seventh goal this season and puts him level with Steven Gerrard for the most scored by an English player in a single Champions League season.
"In these kinds of situations, in my opinion, if we have this game at the Etihad and it's a 3-2 or a 2-2 draw, that won't give us a good feeling going into the next round", he said.
"We have showed we were the better team today and only for a lack of motivation or effort can we not do the same at home".
The Gunners are still in the Europa League and Arsene Wenger's men also have the Carabao Cup final next week against City.
"For a Champions League game we did ever so well".
Both Kompany and Guardiola criticised Basel's Sankt Jakob Park pitch.
Basel threatened in the opening minutes with a brace of counter attacks that could have lead to the first goal.
"I thought the pitch was a bit hard, it was freezing out there", said Kompany while Guardiola described the pitch as "dangerous".
Higuain had put Juventus - finalists twice in the past three seasons - two goals up within the first nine minutes at the Allianz Stadium.