Captain Murray Thomas poked home the only goal 14 minutes from time to give Hearts their third 1-0 win a row. They beat Celtic 3-2 in the game before that.
With under-18s coach Steven Naismith on international duty with Scotland in Austria, Donald Park took charge of the young Jambos for the second game in a row.
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The winning goal from 17-year-old Thomas in the 76th minute was a close range effort following a cutback from James Wilson. The striker also scored the only goal in the 1-0 win away to Hamilton on Friday.
Hearts travel to Celtic on Friday in their next match and have the SFA Youth Cup final against Rangers to look forward to at the end of the season.