The game turned late in the match after Harriers went from looking comfortable winners to falling behind.
Exeter grabbed an undeserved equaliser on 69 minutes when Brock was caught out of position. Stuart Brock
The keeper had driven a poor clearance straight to the opposition and was left stranded as the ball eventually fell for former Manchester Utd man Tomlinson to chip home first time from 30 yards.
And then Exeter took the lead on 74 minutes with a controversial goal from target-man Flack which visibly angered Harriers boss Molby.
Curran's long throw was flicked on by the head of Flack with Brock again caught out and right-back Clarkson tried to hook the ball away before it crossed the line.
However, the assistant referee was in line and immediately signalled the goal for lucky Exeter.
The visitors brought on Broughton for Henriksen 12 minutes from time as they looked to chase the game.
But it was looking increasingly like a game lost and Brock partly redeemed himself with an excellent diving save from substitute's Read 20-yard-drive seven minutes from time.
As Harriers tried to claw their way back into the match they could only muster a Bennett shot from distance that gave Van Heusden a few problems.
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