Crusaders moved above Portadown into third place in the Irish Premiership thanks to a hard-fought 2-1 win over Ballinamallard United at Ferney Park.
Timmy Adamson fired the Crues in front with a low left-foot shot into the bottom corner in the 35th minute.
McCutcheon added the second after 47 minutes with a cool finish after Jordan Owens flicked on a Matthew King cross.
Stafford got the last touch to bundle the ball over the line from a David Kee corner midway through the second half.
Both sides had struggled for league form in recent months with the hosts claiming two points from their previous six Premiership matches and the Crues taking just eight from their last seven games.
With the pitch lightly covered with snow, Clarke set up Adamson to shoot home from the edge of the box.
Alvin Rouse tipped over a Craig McClean header and Liam Martin's sidefooted effort was pushed round the post by Sean O'Neill.
Livewire striker McCutcheon extended his side's advantage soon after the break and then Mark Stafford saw his header from a Cathal Beacom corner cleared off the line.
Owens had the ball in the net but his effort was ruled out for offside, before Stafford gave the Mallards hope of a comeback.
Despite some late pressure, Whitey Anderson's side was unable to find an equaliser and they remain 11th in the table, level on points with ninth-placed Coleraine and 10th-placed Warrenpoint Town.
The Crues lie seven points behind leaders Cliftonville ahead of Saturday's north Belfast derby between the sides, and six behind Linfield.