Falkirk 2-0 East Fife
First-half goals from Darren Dods and Farid El Alagui secured Falkirk's progress to the Scottish Cup fifth round against Division Two East Fife.
Dods fired into the corner of the net from 18 yards after seven minutes.
And striker El Alagui sealed the win in the 21st minute when his header from Kieran Duffie's cross flew past keeper Michael Brown and into the top corner.
Michael McGovern saved Ryan Wallace's shot as John Robertson's men pushed for a consolation goal.