Hearts trip along the M8 ended in their third defeat in four games.
The Gorgie club appointed Daniel Stendel as manager less than an hour their 1-0 defat to Motherwell.
Chris Long fired the home side in front just before the interval, the young striker firing high into the net.
The defeat could have been worse but an Allan Campbell goal in the closing stages was incorrectly ruled offside.
Hearts were reduced to ten men in injury time when Jake Mulraney was dismissed for the visitors for having words with the referee.
Hearts caretaker manager Austin MacPhee: “The period when we’re on top, we need to be more clinical. We’re obviously lacking firepower and the squad is slightly unbalanced – we could do with another wide player. The boys just need to stick together.
“The players are lacking confidence but showed good spirit. They have been really good for me, there is a good culture within the group and whoever inherits that will have a good starting point.”
Motherwell manager Stephen Robinson: “It was a really professional performance. I’m told the second goal was onside and it would have killed the game off. We thoroughly deserved the win
“We are in third place and enjoying it at the moment but I still think there’s more come. It’s my job to manage expectations. We still have to make sure we get enough points to stay in this division, then take it from there.”