Steve Clarke’s side had spent most of the second half on the back foot before Millen found the net in the 73rd minute.
Hearts, who will now be ousted from the Ladbrokes Premiership summit for the first time this season if Celtic pick up at least a point at Livingston on Sunday, had looked lively but struggled to create any clear-cut chances.
The match started off at a great pace and both teams maintained that intensity for the rest of the half.
The visitors wasted a great chance to take the lead inside two minutes, just seconds after Hearts winger Callumn Morrison went down in the box under a challenge from Mikael Ndjoli.
After referee Don Robertson waved play on, Killie broke and Aaron Tshibola set Chris Burke clear through on goal but the winger’s effort was blocked by Hearts goalkeeper Zdenek Zlamal.
Craig Levein’s side enjoyed plenty of possession during the early exchanges but had to wait until the 11th minute for their first sight of goal, with captain Peter Haring rifling a 25-yard volley just wide.
Kilmarnock midfielder Alan Power then fired a shot from distance straight at Zlamal.
A fine move engineered by Hearts forward Steven MacLean carved the away side open in the 20th minute but there were no takers for the striker’s cutback in the box.
MacLean initially dummied Michael Smith’s pass and received a return from Arnaud Djoum before his low cross came to nothing.
Hearts striker Craig Wighton then did well to create space inside the area before crashing a left-footed drive into the side netting.
The Rugby Park outfit continued to look dangerous on the break and a forceful from run from Ndjoli ended with the midfielder firing just wide.
Hearts created their best chance of the half four minutes before the break when Djoum found Ben Garuccio in the box but the left-back’s effort from an angle was well saved by Daniel Bachmann.
Kilmarnock captain Kris Boyd came within inches of giving the Ayrshire side the lead in the 50th minute with a low free-kick from 20 yards that drifted just past the post.
Hearts did most of the pressing in the second half but struggled to conjure up any meaningful openings against a well-drilled Kilmarnock team.
Defender Jimmy Dunne headed on to the roof of the net from a corner before MacLean had a goal disallowed for offside.
After soaking up the pressure, Killie then stormed ahead in the 73rd minute through Millen.
Burke teed up the right-back on the edge of the area and Millen’s well-hit low drive squirmed under Zlamal.
Kilmarnock held on to collect their first league win in four games.of the crossbar but it was Hamilton’s only meaningful effort on goal all game in a dismal display.