The Manchester City goal machine rolls on. On a night when Leicester City supporters were treated to an impressive performance from the X Factor winner Sam Bailey at half-time, it was Manuel Pellegrini's side who hit the right notes on the pitch. A superb free-kick from Aleksandar Kolarov and two goals from Edin Dzeko sealed their passage into the Capital One Cup semi-finals and took the club's tally for the season to a staggering 75 goals from 25 games.

Although Lloyd Dyer pulled a goal back for Leicester 13 minutes from time, any hopes that the Championship club had of causing an upset had long been extinguished. Dzeko's second goal, eight minutes after the restart, put the Premier League club 3-0 up, after which they started to ease off and became a little complacent, giving Leicester the encouragement to believe they could finish with something to show for their efforts.

If Dzeko's opportunist goals were a highlight for City – the Bosnian may sense a chance to get a rare run in the team with Sergio Agüero sidelined for up to eight weeks with a calf injury – the downside for Pellegrini was the sight of Pablo Zabaleta leaving the pitch with a suspected pulled hamstring in the early moments. With Micah Richards already sidelined with the same problem, City will go into the festive programme without an orthodox right-back.

Otherwise this was a routine win for a Manchester City team playing with supreme confidence and, once again, provided a demonstration of the remarkable strength in depth of Pellegrini's squad. The City manager made eight changes from the side who thumped six past Arsenal on Saturday yet the starting XI, who featured Vincent Kompany and David Silva, was full of quality and provided a measure of how seriously Pellegrini views a competition that represents his first opportunity to win silverware in England.

"I think it was a very professional performance," Pellegrini said before expressing his satisfaction at City's average of three goals per game this season. "It's what we try to do. I said some months ago, when I arrived here, that I like my team to play in an attacking way and try to score goals everywhere."

James Milner again showed his worth, setting up two goals in a typically energetic display on the flank. He may yet emerge as a short-term solution at right-back having played in that position for England. On the other flank, Kolarov was playing more like a winger at times and it was his goal, brilliantly curled into the top corner from 25 yards, that got Manchester City on their way in the eighth minute. The only surprise was that it was not until four minutes before the interval that the visitors added a second.

Kasper Schmeichel, playing against the club where he started his career, made decent saves to deny Jack Rodwell and Dzeko before the striker got the goal that he deserved. Having skimmed the upright with a vicious left-footed shot from the edge of the area in the 39th minute, Dzeko prodded home Milner's deflected cross moments later, finishing a fine counterattack started by Jesús Navas.

Dzeko's second owed more to Leicester's lack of concentration. A quick throw-in caught the defence napping and Milner, close to the byline, pulled the ball back for Dzeko to nonchalantly side-foot inside the near post from about 12 yards. Dzeko, who spends more time on the bench than the pitch, now has nine goals for the season. "Every time Edin plays he plays well," said Pellegrini, who named only six substitutes because Stevan Jovetic felt ill on the eve of the match.

While the game was effectively over when Dzeko grabbed his second, Leicester never surrendered and their persistence was rewarded when Dyer drilled a low angled shot that deflected off Kompany and beyond Joe Hart. "We were beaten by a very good side, punished for one or two mistakes," Nigel Pearson, the Leicester manager, said. "The players deserve a bit of credit for trying to put them under pressure and getting a goal back. It would be very easy to let a side of Manchester City's quality dominate and rub salt in the wound."