If Rangers go on to lift the Scottish Cup they will probably look back at last night as the game they effectively won the trophy after Hearts offered them a severe test of nerve at Ibrox.
The final scoreline of 4-1 was convincing enough, but this was a match worthy of being the competition's final as Rangers were troubled for long periods by a Hearts team giving their all.
Ahead of the game, Rangers manager Dick Advocaat had cast doubt on his opposite number Jim Jefferies's negative tactics - but that accusation could not be repeated afterwards.
Rangers were 2-0 ahead inside 17 minutes, through firstly a Barry Ferguson tap-in then an individual effort from Arthur Numan, but Hearts refused to accept their fate. Their self-belief is the strongest of all the sides outside of the Old Firm and by half-time they had halved the deficit through Colin Cameron's 34th-minute penalty.
Hearts continued to press after the restart and with Rangers lacking their usual sharpness in front of goal the prospect of an unlikely replay looked to be looming.
Rangers skipper Lorenzo Amoruso had other ideas however netting on 69 minutes to calm matters and pave the way for a late flurry which saw substitute Billy Dodds score a penalty as Hearts faded.
Earlier, Eoin Jess had kept Aberdeen's hopes of a dream cup double alive with a late strike to shatter Dundee United's hopes for the second time in a month and book the Dons' place in the semi-finals. The Scotland striker was making his first start since suffering ankle ligament damage at St Mirren in the third round in February and did not disappoint with a cool finish when the game looked destined to go to a replay. The visitors have already got next week's CIS Insurance Cup Final against Celtic at Hampden Park to look forward to and now have a place in the last four of Scotland's number one cup competition.