Better from the Championship leaders after a tricky few weeks.
Andy Halliday and Armand Gnanduillet got the goals and others went close, although Robbie Neilson could have done without the nervy last 20 after Dundee's penalty and his team had to dig in a bit.
Here's how they rated out of ten.
Craig Gordon: Two excellent stops with his legs late on after saving from Cummings then reacting well to thwart Sow. 8
Michael Smith: Didn't get forward enough early on but when he did Hearts looked a real threat. 7
Craig Halkett: Solid in the air and tried to step into midfield and play when he was needed. 7
Mihai Popescu: One having one of his better games until conceding a needless penalty. 6
Stephen Kingsley: Tried to get forward and link with Halliday but was less effective than Smith. 6
Andy Halliday: Unlucky not to score early on but kept at it and did well to head home the opener. 7
Andy Irving: Hearts look a more coherent side with him playing, even if he's not at his best. 7
Aaron McEneff: Some really nice clever touches although didn't look like scoring. 7
Gary Mackay-Steven: Was on course to be the villain but set up the winner with a great cross. 6
Liam Boyce: Strong, clever and creative. Very unlucky not to score when he hit the bar. 7
Armand Gnanduillet: Set up the first with a good cross and deserved the luck he got for his own goal. 7
Subs
Jamie Walker: Came on and worked hard. 5
Aidy White: Offered Kingsley late protection. 4
Haring: Came on and was promptly sent off. 2
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