The Motherwell captain announced his retirement earlier in the week but he could not end on a high as goals from Johnny Russell and Jon Daly secured a comfortable victory for United.
Russell opened the scoring in the eighth minute after Darren Randolph had twice denied Stuart Armstrong and the midfielder turned provider with nine minutes to go as he laid the ball to Daly to stroke home from close range.
Craigan was presented with an award prior to kick-off and after five minutes the Fir Park crowd rose to their feet to applaud the Northern Irish centre-back.
After a slow opening to the match, the visitors broke the deadlock. Randolph in the Motherwell goal did well to deny Armstrong on two occasions before Russell bundled the ball over the line from close range.
The home side were dealt a further blow after 12 minutes when Steven Hammell was stretchered off and replaced by Tim Clancy following a collision with Danny Swanson.
United came close to doubling their lead when Russell broke away from Clancy on the left flank and his cut-back found John Rankin, who struck the outside of Randolph's post from a tight angle.
Chris Humphrey was proving to be a handful for the United defence and after a direct run down the right he delivered a dangerous ball in that was handled well by Dusan Pernis under pressure from Jamie Murphy.
The Jamaican was involved again minutes later when he took on Daly and delivered a neat cross along the six-yard box, but to the dismay of the home support nobody was on hand to turn the ball in.
Michael Higdon was next to come close to grabbing an equaliser for Motherwell but was adjudged to have strayed offside when trying to meet Humphrey's delivery.
Paul Dixon clipped the top of Randolph's crossbar with an excellent free-kick five minutes before the interval before Higdon came agonisingly close to levelling the game when he powered a header just wide of the target following a pinpoint delivery from Tom Hateley.
Steven Jennings blazed an effort well over the bar in the opening minute of the second half as the hosts began on the front foot.
Swanson became the first United player to receive a yellow card after a careless challenge on Keith Lasley and he was fortunate to escape a further caution a minute later following a mistimed tackle on Clancy.
Peter Houston reacted by replacing Swanson with Ryan Dow and the midfielder almost made an immediate impact, when he struck just over after collecting Scott Robertson's pass.
Randolph produced a wonderful piece of goalkeeping to keep out Daly's curling effort just before the hour mark and Dow again went close after connecting with Dixon's cross on 63 minutes.
Craigan saw his shot from the edge of the box drift just wide of the left-hand post, the second time he had come close to netting on his final appearance.
Gary Mackay-Steven came on for Armstrong in the 67th minute and the winger blasted inches wide within a minute of his introduction.
Robertson passed up a glorious opportunity to extend the visitors' lead after being released by Russell just inside the area, however, the midfielder struck well over the top.
Craigan took his final bow after 78 minutes when he made way for Ross Forbes, who will also leave Fir Park at the end of the season.
United doubled their advantage with nine minutes remaining, Russell set up Daly, who had the simple task of rolling the ball into the net.
Russell was replaced by Ryan Gauld for the closing stages and the visitors continued to look for goals.
Mackay-Steven saw his shot deflected wide by Shaun Hutchinson and John Rankin's long-range strike could not find the target.
Higdon's disappointing day continued when he fired well wide in the closing minute and the Fir Park side were unable to threaten during the final minutes, ensuring United left Fir Park with all three points.