Connor Young broke the deadlock for the Light Blues early in the contest, but the Gers were pegged back midway through the second half.
However, David McCallum’s side kept their poise and they were rewarded when goals from Arron Lyall and Robbie Ure late on sealed all three points.
McCallum named six changes to the side that faced Liverpool in the UEFA Youth League in midweek, with Greig Allen, Johnly Yfeko, Bailey Rice, Arron Lyall, Connor Young and James Graham coming into the starting lineup.
Aaron Lyall threatened just minutes into the contest, sending a powerful effort just wide of the post as the young winger set his stall for the afternoon.
Jack Harkness’ cross then narrowly evaded a lurking Zak Lovelace in the six-yard area, with Cameron Quate in the Edinburgh University goal making a vital intervention.
The Light Blues took the lead on 13 minutes through Connor Young. Neat interplay from Lyall and Harkness seen the ball pulled back to the edge of the area. The 18-year-old faked to shoot one way before checking onto his right foot and curling his effort in off the post.
The frame of the goal was struck again just minutes later. Lewis MacKinnon powered a header off the far post before Zak Lovelace cracked the upright from a tight angle with the rebound from six yards out.
The Gers almost doubled their lead from a corner when Charlie Lindsay’s delivery narrowly missed Greig Allen who was well placed in the penalty area.
Graham then skimmed the outside of the far post with an effort similar to Young’s opener, manufacturing space before curling a dangerous effort to the goalkeeper’s left.
Lewis Budinauckas was called into action for one of the first times in the game when he was quick off his line to smother a promising Edinburgh University attack.
The Young Ger was also equal to James Lawton’s low driven effort from distance, before the home side almost made it two on the afternoon.
Lyall found Lovelace in space inside the penalty area but, after collecting in space, the Rangers forward could only steer his effort straight at the goalkeeper.
Patrick Baird then struck the post under pressure from Allen after a pull-back down the right for the visitors.
Edinburgh University equalised on the hour mark. Keir Foster floated a cross in from the left where David Maskrey powered his header into the ground and beyond the reach of Budinauckas.
McCallum made a triple substitution immediately afterwards, withdrawing Lindsay, MacKinnon and goalscorer Young for Ross McCausland, Kevin Ciubotaru and Connor Allan.
Allan almost made an instant impact when his pull-back was met by Lyall, but the Edinburgh University goalkeeper was equal to the attacker’s effort.
McCausland then created danger on the left-hand side, cutting in off the flank before drawing a diving stop from Quate down to his right.
The substitute combined with Lovelace shortly after, running onto the Englishman’s pass before flashing his finish inches wide of the far post.
Lovelace was involved in another promising combination minutes later, receiving substitute Robbie Ure’s lay-off inside the danger area, but Edinburgh University were able to clear it for a corner.
Rangers’ endeavour was rewarded in the 77th minute as they restored their advantage. The Light Blues worked the ball into a congested penalty area before McCausland picked out Lyall in space, with the Gers youngster working the ball onto his left foot and sending an unerring finish into the bottom corner.
McCallum’s side then extended their lead late in the match to seal the victory. McCausland turned provider once again, slipping Ure through on goal before the Gers forward coolly rounded the goalkeeper and slotted into an empty net.
RANGERS: Budinauckas, Harkness, MacKinnon (Ciabotaru, 62), Allen, Yfeko, Rice, Lindsay (Allan, 62), Young (McCausland, 62), Lyall, Lovelace (Strachan, 82), Graham (Ure, 71)
SUBS: Pazikas, Ewen
EDINBURGH UNIVERSITY: Quate, Thomson, Paton, Maile, McDonald, Murray, Maskrey (Grey, 77), Dick, Anderson (Foster, 45), Baird, Lawton
SUBS: Koutalides, Bannon, Brindley
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