Sammy Clingan had given the visitors an early first-half lead, which held until Ryan McGivern equalised in the 84th minute.
Jude Winchester then restored the away side's advantage straightaway before Leigh Griffiths flicked in an equaliser under 60 seconds later.
The two teams are scheduled to meet in the William Hill Scottish Cup on Sunday and for Fenlon, the draw highlighted the similarities in quality that exist in the two SPL sides, with both fighting for the win to the end.
"We never give up hope with these players," said Fenlon. "They always keep on going till the end. To be fair I thought we deserved a draw from the game.
"The game there shows there is little between the teams and it'll be a tight game on Sunday. We're right up for it and we'll have a big travelling support behind us.
"Hopefully the pitch is a bit better than ours and we can go play some decent football, although to be fair we did at times."