Killie had the chance to open the scoring from a 20th-minute free kick, from which Finland international Alexei Eremenko came within inches of finding the top corner.
The visitors had Samson to thank for keeping them on level terms just before the half-hour mark when he pulled off an exceptional save to deny Ali Crawford from close range.
Both sides finished the half strongly, with Mackinnon forcing Samson into another good stop minutes before the break, while Rory McKenzie twisted and turned in the Accies box and tested Michael McGovern with a curling strike.
Kilmarnock came out of the tunnel the more confident of the two sides and almost took the lead within minutes of the restart as Craig Slater's drive whistled past the Hamilton post.
Hamilton could have stolen maximum points in the final 10 minutes as Scotland almost had a sight of goal, only for a vital interception by Mark Connolly to deny him the chance to go one-on-one with the goalkeeper.
The result leaves Hamilton in fifth place in the table, with Killie down in eighth.