City saw little of the ball early on, however, as the home side enjoyed the better of the opening 20 minutes and Hart had to be at his best to deny Jones after the midfielder fired a shot across goal.
Backed by a vociferous home crowd Schalke continued to press and cause City problems with Micah Richards blocking Heiko Westermann's goalbound effort and the lively Jones again testing Hart with a volley from 20 yards.
At the other end Darius Vassell tried his luck from distance, but City did take the lead against the run of play 10 minutes later.
The visitors had rarely threatened but Vincent Kompany sent Sturridge clear and the 19-year-old took his time before crossing low for Benjani to score from six yards.
Spurred on by the goal City upped the tempo and threw men forward in search of a second.
They thought they got it as Ireland turned in Sturridge's shot after another swift attack, but the midfielder was flagged offside.
Despite their attacking intent City remained solid at the back and continued to frustrate the hosts in the second half.
Schalke, restricted to a few pot shots from distance, were always wary of the threat posed by Mark Hughes's team on the break and Shaun Wright-Phillips stung the fingers of Manuel Neuer with a shot from 25 yards after a surging run.
A deserved second goal soon came though as Ireland capped an impressive all-round display with his eighth goal of the season.
The midfielder was an elusive presence in midfield and he coolly slotted the ball past the on-rushing Neuer after ghosting in following a one-two with Benjani.
A rare moment of alarm for City in the second period saw Asamoah head goalwards, but Hart was on hand to deny the striker as he flew to his right to block the shot.
Manchester City manager Mark Hughes:
"It couldn't have gone any better for us, we had a game plan and the players executed it perfectly - it was a very accomplished performance.
"We were really comfortable out of possession, got our shape back very quickly and looked to break with pace and that's what we did on my occasions causing them some real problems.
"In the end I think they ran out of ideas because they were conscious of the fact that we had a real threat going the other way."
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