City are now through to their first quarter-final in the competition since losing 2-1 to Ipswich (aet) in the 2000-01 season.
Sven made two changes with Swedish keeper Andreas Isaksson making his first appearance of the season in place of Joe Hart, while Michael Ball came in fro Martin Petrov.
The Bulgarian winger failed to recover from a toe injury and Ball came in at left-back, with Javi Garrido moving forward into left midfield.
There were few chances at the Reebok, with City's Michael Johnson missing the best chance of the first half.
And only Elano's late winner prevented the game going to extra-time.
Bolton were incensed as referee Howard Webb consulted his assistant before awarding a penalty for handball by Bolton sub Lubomir Michalik.
Elano then stepped up to place the spot-kick wide of Jussi Jaaskelainen for his 5th goal of the season.
Bolton's El Hadji Diouf then smashed a free-kick against the City crossbar and despite five minutes of stoppage time, City managed to hold on.
Influential City defender Micah Richards had been stretchered off late in the second half. At this stage it is unclear what and how serious the injury is.