Robbie Weir's early own-goal gave the Sky Blues the lead, and they dominated the game against Stephen Baxter's side, who struggled to impose themselves on proceedings.
But deep into stoppage time Robinson poked home from a Jonny Tuffey flick on to take the game into extra time.
The Seaview side dominated the additional 30 minutes, but just when it looked like the game was heading to penalties up stepped McMurray, who blasted home a superb volley to win the cup and a place in the Europa Conference League qualifiers for the Crues.
It was cruel on Ballymena United who were excellent on the day but Crusaders hung in there to grab a famous victory.
The Crues made the early running with Jordan Forsythe going close with a header from a Ben Kennedy Corner in the opening minutes.
But the Sky Blues soaked up the early pressure and fashioned a great opportunity of their own on eight minutes.
Andy McGrory's clever through ball split the Crusaders defence allowing Leroy Millar to run in on goal, but his shot was deflected wide by Jonny Tuffey.
Ballymena broke the deadlock from the resulting corner though as McGrory's inswinger was diverted into his own net by the unfortunate Weir at the near post.
The goal shook the Crues with Ballymena in the ascendancy and unfortunate not to add to their lead but for a couple of close offside calls.
Stephen Baxter's men eventually found their rhythm again and almost levelled matters on 27 minutes but for a superb save by Jordan Williamson at his near post, pushing away Ben Kennedy's curling free kick.
The went close again 11 minutes before the break as Adam Lecky flicked on for Paul Heatley, but Redman did well to get back and deflect the forward's shot over the bar.
From the resulting corner the ball dropped for Jordan Forsythe, but his goal-bound effort was blocked by McGrory.
Crusaders almost shot themselves in the foot as we approached half-time.
Billy Joe Burns and Daniel Larmour dallied after a long punt forward by Redman, Burns scuffed his attempted back pass to Tuffey allowing Parkhouse to steal a march, but to his credit the experienced defender recovered well to get back in and nick the ball again after the Ballymena man had gone around the keeper.
Robinson was introduced at the break, and his first involvement was to concede a free kick 20 yards from goal which McGrory curled narrowly wide of the target.
The Sky Blues went close again on 51 minutes as Josh Kelly won the ball in his own half before surging forward and feeding Steven McCullough, whose low ball in was fired over the bar by Ryan Waide.
Crusaders were struggling to fashion out any opportunities against a resolute Sky Blue defence.
They did finally get in behind on 63 minutes but Williamson stood up to push away Heatley's effort.
The Sky Blues were looking for a penalty when substitute Paul McElroy went down under a tackle from Burns with 19 minutes to go, but the defender just got his studs to the ball and play was waved on.
Just when it looked like Ballymena had withstood the Crusaders pressure up popped Robinson with a 93rd minute equaliser.
The big defender touched the ball home at the back post after goalkeeper Tuffey had flicked on Heatley's corner.
Andy McGrory had to be alert to prevent a tap-in for Heatley on 97 minutes as the Crues started to dominate in extra time.
Ballymena spurned a great opportunity at the start of the second period of extra time as they broke four on two, but Kenny Kane dallied too long in the box and Robinson blocked his shot.
Crusaders were still providing an aerial threat and substitute Aidan Wilson rattled the bar with a header with five minutes to go.
There was more late drama to come. Just as they had done at the end of normal time the Crues popped up with another late goal to win the cup.
This time it was Ballymena United old boy McMurray, who slammed home a volley to send the Crues support into raptures and secure the Irish Cup for the Shore Road men.
Ballymena United: Williamson, Redman, Kelly (Henderson 82), Waide (Place 91), McCullough, Barr (McElroy 71), McGrory, Parkhouse (Kane 78), Keeley (Loughran 78), Millar, Graham.
Subs: Johnston, Smith.
Crusaders: Tuffey, Burns (Doyle 87), Weir (Robinson 46), Lowry (Owen 81), Kennedy, Lecky (Caddell 68), Forsythe, O'Rourke, Larmour (Wilson 110), Heatley, Clarke (McMurray 68).
Referee: Tony Clarke