A late rally by nine-man Hearts failed to bring at least a goal that would have been a deserved reward in Forfar.
Hearts fielded a mixed squad that included Jack Hamilton, Brad McKay, Jordan McGhee and also Kenny Anderson, making his under-20 debut for the club. Included among the substitutes was Sean McKirdy, making a comeback after being out since damaging a hamstring last December.
One goal separated the sides at half-time, Greg Warwick scoring with a 20-yard shot into the corner of the net.
Hearts coach Jack Ross made two changes at half-time that led to a much better performance in the second period.
Robbie Buchanan missed a possible chance shortly in to the second half, stumbling over the ball with only the keeper to beat, and Hearts paid for this on 56 minutes when Calvin Colquhoun thundered home a 30-yard shot.
Nathan Flanagan fired a shot wide as Hearts pushed forward. On 79 minutes Gary Oliver flicked a shot against a post, but three minutes later Alistair Roy pulled a goal back rifling home a Flanagan through ball past. Thirty seconds later Liam Henderson was sent off for pulling back Dundee’s Ryan Gemmell, who was through on goal, but Hearts were still the better side even although reduced to nine men when Daniel Baur was forced to leave the field for the last five minutes.
Hearts: Hamilton; Hutchings (Flanagan 46), McKay, Baur, Henderson, Buchanan, McGhee, Baxter (McKirdy 46), Moore (Roy 82), Anderson, Oliver. Unused subs: Mason GK, Morrison.