Murray, who left Dumbarton to become St Mirren’s new boss on Friday, looked on from the stands and saw a display that offered little going forward bar a brief first-half spell.
And their defensive stand was finally broken seven minutes from time when Crawford, after wasting a couple of earlier chances, broke the deadlock with what turned out to be the only goal.
Hamilton started brightly and went close to an opening goal when Dougie Imrie tried his luck from outside the box, but Marian Kello made a smart save.
But relegated St Mirren looked keen to impress their new manager and spent 15 minutes on the front foot, when they twice could have taken the lead – Jack Baird’s close-range effort failed to hit the target and Stephen Mallan rattled the bar with a free-kick.
The Accies finished the first 45 minutes the stronger, though, with Jesus Garcia Tena also denied by the frame of the goal, again with a direct free-kick, and the influential Crawford having two efforts turned away by Kello.
St Mirren’s Slovakia ‘keeper was again worked just before the interval when a shot from Louis Longridge had him scrambling after it went through Jason Naismith’s legs.
Chances were few and far between in the first 15 minutes of the second half, although Imrie again was not far off target with a low drive just past the post and Lucas Tagliapietra headed wide.
By now St Mirren were struggling for any fluency and Accies ‘keeper Michael McGovern was a virtual spectator as his side started to completely dominate.
After a series of substitutions, Hamilton continued in the ascendancy and they eventually got their breakthrough seven minutes from time.
The game’s two best players combined for the goal, with Imrie playing in Crawford outside the box and the midfielder curled a shot into the corner of the net past a despairing Kello for his 11th goal of the season.
Longridge had a chance to make it 2-0 but was denied by Kello, however with St Mirren failing to muster any efforts on goal, the Accies had little bother hanging on for three points to finish the season as clear winners of the bottom-half table.