Paraguay striker Santa Cruz has struggled with injury since his arrival from Blackburn in the summer, but he marked his first start for the club by restoring City's first-half lead after Scunthorpe had briefly drawn level.
City enjoyed a dream start on home soil as Stephen Ireland effortlessly curled his shot from the edge of the area inside the upright after just three minutes.
But Championship side Scunthorpe played some neat stuff at times and equalised on 26 minutes after a quick exchange of passes resulted in Jonathan Forte scoring from close range.
Mark Hughes' men were back in front before half-time, though, when Santa Cruz was picked out unmarked by Pablo Zabaleta's right-wing cross, and he headed back across goal and beyond Iron keeper Joe Murphy.
Joleon Lescott headed City's third goal from a Shaun Wright-Phillips corner on 56 minutes and Carlos Tevez turned home from close range after a quickly-taken corner on 71 minutes.
The rout was completed on 77 minutes when substitute Michael Johnson - making just his second appearance in over a year - lashed home a left-footed shot from 25 yards to send City through to the last eight with a flourish.
City made six changes from the side that drew with Fulham on Saturday.
Kolo Toure and Martin Petrov were both injured, with Micah Richards, Wayne Bridge and Craig Bellamy on the bench and Emmanuel Adebayor rested.
Scunthorpe had David Mirfin back after a bout of sickness. Martin Woolford also came into the starting line-up, Jordan Spence and Sam Togwell reverting to the bench.
Noisy fansScunthorpe had 4,000 noisy fans with them, and they were boosted by a second minute drive from Paul Hayes that Shay Given saved, with some difficulty, to his left.
But a minute later Scunthorpe were guilty of standing and watching as City swept into their half, Wright-Phillips finding Ireland to his left.
The midfielder cruised on, unchallenged by any defender to calmly guide the ball past Murphy from the edge of the box.
Wright-Phillips twice soon after could have extended the lead with efforts from the edge of the box.
Scunthorpe were barely able to get out of their half at this stage, such was the pace and pressure of City's attacks. But they were competitive and organised and they weathered the initial storm.
When Scunthorpe did get into a danger area, they scored an outstanding equaliser after 26 minutes.
Nigel de Jong gave the ball away in midfield, and it was swept out to Marcus Williams, racing away on the left. His neat ball into the six-yard box evaded Lescott and found Forte, who finished with ease from a couple of yards.
Hayes had a great chance with a header, saved by Given, before Ireland sent in Wright-Phillips for a shot that Murphy blocked with his legs.
But Scunthorpe had lost their star-struck look by now and were moving forward with a growing confidence. Hayes again, arriving on the far post for a hook shot wide, had City stretched as the Iron continued to grow in confidence.
But City were back in the lead after 38 minutes. Zabaleta sped down the right, wrong-footing Hayes as he went. And when the cross arrowed into the box, Santa Cruz stepped away from Woolford before rising to plant a headed back into the far corner.
Scunthorpe replaced skipper Rob Jones with Niall Canavan at the break. And they were still prepared to run at City's back-line.
But the quality of City's attacking play almost produced a third when Ireland raced through from midfield before slipping the ball to Tevez, the shot deflecting inches wide.
Breathing spaceThen the impressive Ireland created another opening, setting up Santa Cruz for a drive beaten away by Murphy. And it took a header almost on the line to stop a cross reaching Ireland.
But from the resulting corner from Wright-Phillips, Lescott rose unchallenged 12 yards out to guide a fine header into the top corner to give City the breathing space they wanted after 56 minutes.
Canavan then had to kick off the line from Ireland, as the midfielder rolled a shot wide of Murphy. City sent on 19-year-old Vladimir Weiss in place of Ireland.
Scunthorpe wilted now under the constant pressure, and Tevez crowned a fine display of ceaseless running by prodding home another corner after 71 minutes, again criminally unmarked.
It was a cruise now, and substitute Johnson - coming on for only his second game of the season in place of Gareth Barry - unleashed a rising 25-yarder that soared into the top corner for the fifth.
Tevez was replaced by Benjani after 78 minutes, to a deserved standing ovation as City threatened to run riot at the end.
Manchester CityTeam StatisticsScunthorpe United5Goals121st Half Goals19Shots on Target47Shots off Target42Blocked Shots17Corners18Fouls82Offsides12Yellow Cards00Red Cards082.8Passing Success74.928Tackles1878.6Tackles Success72.258.3Possession41.754.9Territorial Advantage45.1