The sides could not be separated in a 2-2 draw first time round, meaning a replay was required between the Irn-Bru Scottish Football League Championship First Division rivals.
The tone for a fine encounter was set in just the third minute, when Ryan Donnelly found Josh Watt, who curled home from just inside the penalty area.
However, Airdrie hit back immediately, Greig Spence firing home and Allan Walker converting a penalty after Nathan Blockley had brought down Simon Mensing.
Yet, just before the interval, Paul Di Giacomo matched that effort from the spot following Laurence Ellis' foul on Donnelly to level matters.
Grant Anderson fired home to put Rovers back in front just after the break, only for Gregor Buchanan's header four minutes from time to ensure an extra 30 minutes.
Yet it was Raith and Hill who were to have the final say as the defender delivered a decisive header to set up a fourth-round clash with Deveronvale.
Four goals in 17 minutes either side of half-time helped Stenhousemuir storm back from behind to down 10-man Berwick 5-2.
As in the original tie, Irn-Bru Third Division outfit Berwick took the lead against their Division Two opponents in pursuit of a fourth-round encounter with Division One Falkirk.
Lee Currie drilled home a clinical 11th-minute penalty after Craig Anderson brought down Stuart Noble, but Stenny were level six minutes before the break when Darren Smith nodded in Sean Dickson's cross.
Dickson was involved again early in the second half, Youssef Bejaoui in the Berwick goal parrying his 20 yarder to leave John Gemmell with a simple headed finish.
Stewart Kean levelled for Stenhousemuir in the first game and a pair of close-range finishes appeared to put the match beyond doubt before Darren Lavery gave the hosts hope.
Lavery's calm effort was laid on by Currie but midfielder would not see the end of the match, picking up a second booking for fouling Smith moments after the Stenhousemuir man added his second from 12 yards with four minutes to play.
Michael Tidser bagged a second-half brace as Morton eased to a 3-0 replay victory over Albion to secure a fourth-round trip to Turriff United .
The sides played out a 1-1 draw in the original tie and Albion's David Crawford drew a sharp save from Morton goalkeeper Derek Gaston in the 19th minute.
David Graham should have put the hosts ahead when he volleyed wide on the stroke of half-time, but a dominant second-half display meant he would not rue his profligacy.
Graham was the provider in the 51st minute, crossing from the left for Martin Hardie to plant a header high beyond Matthew McGinley.
Barely a minute later, Tidser converted Fouad Bachirou's pass to leave the visitors reeling.
And Tidser completed Albion's misery 19 minutes from time when David O'Brien teed him up to crash home emphatically from the edge of the box.