David Silva and newcomer Nolito scored the other goals for City, in what was an excellent debut in Europe for new coach Pep Guardiola.
“We are almost in the Champions League. That was our target. It was a great performance, great attitudes,” the former Barcelona and Bayern Munich coach said.
“The result is amazing. I am so satisfied with the way we played – a big compliment to these fantastic players. All the managers in the world want to create chances and concede few.”
Meanwhile, playmaker Kevin de Bruyne said: “I think we played a really good game. It could have been eight or nine. In the end Sergio Aguero scored three goals. If you do that, nobody will complain about the two missed penalties.
“Now we know it’s a really good advantage and we should qualify next week.”
Aguero’s first penalty was well saved by Steaua keeper Florin Nita. Then his second one, just 10 minutes later, hit the crossbar and went over.
However, Aguero soon made amends with his impressive hat-trick, as the brittle local defence quickly fell apart.
In Tuesday’s other first legs, Borussia Moenchengladbach won 3-1 at Young Boys – on a brace from Raffael plus a goal from Andre Hahn – while Copenhagen edged APOEL 1-0 on a goal just before half-time from Andrija Pavlovic.
“To win 1-0, without conceding at home, is a very good result for us,” Pavlovic said.
“Things will be difficult for us in Cyprus (in the second leg) but I think we are in a good position to go through now, if we play well there.”
Meanwhile, Ajax came from behind to draw 1-1 with Rostov, thanks to an equalizer from Davy Klaassen, while Dynamo Zagreb forced a 1-1 at home to Salzburg courtesy of a late leveller from Marko Rog.
The second legs will be played August 24.
Wednesday will see five other play-off first legs, with Villarreal taking on Monaco and Porto hosting Roma.
Source: GNA/News Ghana