The young Gers went ahead twice in the contest through goals from Ross McCausland and Josh McPake, but the Premier League 2 outfit responded to snatch victory at the death.
There was a late change to the starting lineup when Thompson Ishaka dropped out due to injury and was replaced by Paul Nsio, with Rangers making six changes from the midweek triumph over Spartans in the SPFL Trust Trophy.
Early encouragement for the Light Blues arrived when Zak Lovelace was released into a promising area by McCausland, although the Englishman was fouled outside the penalty area.
McCausland then turned scorer just minutes later to break the deadlock in Manchester, latching onto Bailey Rice’s expertly weighted through pass and slotting home.
However, the visitors were pegged back just shy of the half-hour mark, before Lovelace went close when he pinched possession in an advanced area and drew an impressive stop from the City goalkeeper.
The young Gers restored their advantage with seven minutes remaining before the interval as McPake slammed home from the edge of the penalty area.
City responded on the stroke of the half-time whistle, with David McCallum shuffling his pack and introducing Connor Allan in place of Yfeko.
Lewis Budinauckas produced a fantastic diving save to keep the home team at bay just minutes shy of the hour-mark as City put together a string of promising attacking moves.
The young Gers goalkeeper was called into action again to deny a dangerous header, before McCausland and McPake combined down the opposite end only for the linesman to cruelly raise his offside flag.
The later sucker punch then arrived three minutes from time as City went ahead for the first time on the afternoon to secure the victory.
RANGERS B: Budinauckas, Devine (Hutton, 63), King (Allen, 63), Yfeko (Allan, 45), Fraser (Newton, 83), Rice, Lyall, McCausland, Nsio (Strachan, 83), McPake, Lovelace
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