It took Premiership Motherwell 30 minutes of extra time to see off an impressive showing from League Two East Fife.
East Fife started brightly and almost took a shock lead within a couple of minutes when Well keeper Connor Ripley was inches away from blasting a clearance straight off the in-rushing Nathan Austin.
Austin was looking lively up front for Gary Naysmith’s men, and he robbed Lois Laing of possession as the Well defender dithered over his clearance.
His eventual cross was cleared from a corner from which Jonathan Page’s header cleared the bar by only inches.
Motherwell were presenting little in an attacking sense and, as the first half went on, their supporters grew more frustrated.
Matters weren’t helped as a series of straightforward passes were wasted by the out-of-sort visitors.
Ian Baraclough’s men couldn’t have been any worse in the second half than they were in the first, so the gaffer introduced the lively Dominic Thomas from the break.
The 19-year-old added the spark the Premiership side had been missing and it was the Methil men who found themselves having to do the defending.
That didn’t last, though, and Well quickly found themselves on the back foot again.
Kyle Wilkie and Austin had posed problems for the visitors all night and the duo combined well to break the deadlock.
Wilkie broke free of his marker and picked out Austin on the edge of the area, who curled a fine shot around Ripley.
As was to be expected, Motherwell started rushing forward in numbers, and a decent Ryan Goodfellow save from Louis Moult kept the scores level.
Moult wasn’t to be denied, though, and just a couple of minutes later he did even things up when he beat Goodfellow from 18 yards.
The goal forced the game into extra time.
Wilkie almost restored East Fife’s advantage when he weaved around the visiting defence and sent a shot towards goal which Ripley did well to tip around the post.
Scott McDonald posed a constant threat when he came on and put his side into the lead for the first time in the tie when he drilled past Goodfellow.
The Fifers had put up a brave performance, but as extra time dragged on Well stretched their lead through Lionel Ainsworth.
East Fife: Goodfellow, Slattery, Page, Walker, Brown, Austin (Sutherland 90, Smith, Wilkie, O’Kane, MacGregor (Naysmith 82), Mercer. Subs Couser, Mullen, Murray, Sutherland.
Motherwell: Ripley, Law, Chalmers, Kennedy, Laing, Lasley, Leitch, Moult, Clarkson (McDonald 61), Johnson (Thomas 46), Ainsworth. Subs – Twardzik, Cadden, McManus, Watt, Taylor.