The 19-year-old Nigerian, restricted mainly to substitute appearances this season, put City ahead from close range after four minutes, converted a penalty after 24 minutes and raced clear to complete his haul late on before Raheem Sterling also got his name on the scoresheet.
With leading striker Sergio Aguero not required from the bench having been rested for the fourth round tie, Inheanacho's display augured well for City as they chase silverware on four fronts and proved exactly why Pellegrini was content to allow Edin Dzeko and Stevan Jovetic to leave on loan.
"Kelechi is a very good young player. We let (Stevan) Jovetic and (Edin) Dzeko go because I see Kelechi every day and know what he can do," Pellegrini told City's website.
With Dzeko at Roma, Jovetic at Inter Milan and Kevin de Bruyne out injured, Inheanacho could find himself called upon as City's season comes to the boil in the next few months.
Pellegrini hinted on Saturday that Inheanacho, who has now scored nine goals in five starts in all competitions this season, could be included in City's Champions League squad when the competition resumes next month.
City, who are second in the Premier League and in the League Cup final, have to submit any amendments to their Champions League squad to UEFA on Monday.
They face Dynamo Kiev in the last 16.
(Reporting by Martyn Herman)
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