Pep Guardiola's side were simply breath-taking as they blew their Swiss opponents apart in a blistering opening period.
The second leg is live on BT Sport on March 7.
"We are still in February and in the Premier League we are in an fantastic position and we are nearly in the quarter-finals, we are in one final [Carabao Cup] and on Monday we have the opportunity to reach the quarter-finals of the FA Cup. Game by game", said Guardiola.
The visitors' second goal followed just four minutes later. Last season we missed him a lot when he was injured.
"I thought the pitch was a bit hard, it was freezing out there", said Kompany while Guardiola described the pitch as "dangerous". He doesn't feel the pressure.
The emphatic nature of the victory means Guardiola may be able to rest players in the second leg but he is not looking that far ahead yet. With AP Photos.Manchester City beat Basel 4-0 away in the first leg of their Champions League last-16 match.
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Vinny (Kompany) is back, Fabian (Delph) is back - a lot of players have come back from long-term injuries.
Chelsea FC return to FA Cup action with a fifth round clash against Hull City at Stamford Bridge on Friday night. Gabriel is coming back soon.
Speaking after the game in Switzerland and assessing a varied schedule to come, he said: "It's so important".
Basel head coach Raphael Wicky opted to play a back five when the host were defending, but the ploy only failed to keep City out for the first 14 minutes.
Higuain had put Juventus - finalists twice in the past three seasons - two goals up within the first nine minutes at the Allianz Stadium.
If there was one criticism of Gundogan this season it was that he is simply not decisive enough in the final third. "We have got a return game to have another good performance".
Basel defender Leo Lacroix stopped Fernandinho, but the ball fell into Aguero's path who hit the bottom corner from outside the area on 23 minutes.