Abdallah Sima, on loan from Brighton, scored the crucial goal after 34 minutes – his 12th of the season – but also missed a chance with striker Danilo and left-back Ridvan Yilmaz, among others, wasting opportunities.
The Light Blues remain eight points behind leaders Celtic having played a game less and the Belgian has now gone 11 matches unbeaten since becoming boss but noted the possibility of a Jambos equaliser.
“For sure it’s a very important win,” said Clement, who revealed midfielder Tom Lawrence would be assessed on Thursday morning due to a muscle injury.
“We created a lot of chances but that’s still a working point.
“We need to be more clinical. We need to kill off the game if we can and get the second goal, it would have been a different end to the game because it allowed Hearts to stay in the game and with every long ball or long throw, they were looking for the chance that drops to someone’s feet to finish off.
“We had five big chances but for me, with our qualities, it should be at least three goals. So more things to work on.”
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