The Bhoys netted the opener midway through the first half when Ewan Henderson dinked the ball past Brian Kinnear from close range.
However, just before the break, the light blues scored a surprise equaliser when Matthew Shiels finished expertly by Ryan Mullen.
Celtic ruined any chances of a possible comeback when Jack Aitchison scored from a low drive in the 69th minute.
There was to be late drama when Celtic went down to 10 men after Kerr McInroy was given a second yellow card.
The Parkhead club survived the scare to run out winners of the Glasgow Cup for the fourth straight year.
Dominant Celtic given late shake at the end of first half
Six minutes into the first half produced the first chance with Gers captain Jordan Houston denying Henderson a clear goalscoring opportunity.
Celtic took the lead 11 minutes later when Henderson got the better of Houston but was made to work for his goal.
The scorer's first attempt was parried out by Kinnear, however, Henderson followed up to slot into the free net.
Rangers almost found an immediate response when forward Zak Rudden was denied by the legs of Mullen from close range.
Rangers found their feet as the half drew to a close and were duly awarded with a goal just before the whistle.
Starlet Billy Gilmour's smart play around the Celtic penalty area allowed Stephen Kelly to shift off his man and play in the waiting Shiels to slot into the bottom right corner.
Rangers stronger but receive Celtic sucker punch
Seven minutes into the second half and Rangers almost went ahead with Rudden charging into the box only for a last-gasp tackle by Celtic captain Robbie Deas to deny him shot at goal.
Shiels could have claimed a second of the match when his long-range effort was deflected into the arms of Mullen.
Up against the ropes, The Celts took a surprise lead when Aitchison's low drive sailed by Kinnear at his right-hand side.
Rangers' hopes for a late leveller increased when Celtic were a man lighter three minutes before the regulatory 90.
Arguable man of the match McInroy was given a second yellow card much to his bemusement, leaving his team to show character to see the rest of the game out.
A late Gilmour free-kick deep into the box met the head of substitute Matti Zata but the ball narrowly went over the bar.
The first teams lock horns this Sunday at Hampden in the Scottish Cup semi-final, while some of the youngsters from this fixture will hope to appear in next week's Youth Cup final between the two.