There were six changes to the Well side that beat Gretna on Saturday, with Martyn Corrigan, William Kinniburgh, Brian McLean, Simon Mensing, and Darren Smith all given their first starts and Chris Porter restored to the starting line-up.
Both sides made good chances in the opening minutes, with Steve Hislop's cross-cum-shot clipping the cross bar for Rovers and Chris Porter firing a header wide for Well.
The visitors almost opened the scoring on 14 minutes but Keith Lasley was well placed on the post to clear Marvin Andrews' net-bound header. Raith were the better side for much of the early stages without having the quality to test Graeme Smith in the Well goal.
At the other end Ross McCormack sent a weak header wide, Porter saw a shot saved from 12 yards out.
Raith keeper Chris Fahey looked to have kept the score level at the break when pulled of an excellent full-length save to deny McLean from a Lasley corner.
But as the clocked ticked on to 45 minutes the same pair combined and this time Fahey was left helpless from McLean's well-placed header.
It didn't take long for Raith to equalize after the break, they gave Well a warning after only a minute when Derek Carcary raced clear only to be denied by Smith.
Within minutes Carcary got his goal when he skipped past Kinniburgh on the by-line before shooting low past Smith from an acute angle.
Both sides made a number of chances with Raith looking dangerous on the break, but they were hit on the break themselves in 74 minutes.
Jim Paterson burst down the left before picking out McCormack 20 yards out, the Well striker steadied himself before sending a low shot past Fahey.
Motherwell sealed their progress to the next round with a third in stoppage time, Porter latched on to a loose ball and headed for goal where he slid the ball past the advancing keeper.