After several missed chances from both sides, Scott Sinclair eventually broke the deadlock in the 60th minute when he fired home from close range.
The winger completed his brace four minutes later after his shot was deflected into the net to give the Bhoys a comfortable lead.
Ambrose then started the fightback against his former team after he struck past goalkeeper Craig Gordon in the 76th minute.
And with 11 minutes before full time, Oliver Shaw beat his marker before latching home to help Neil Lennon’s men to a share of the spoils.
The Nigeria international has featured in all the league matches for the Edinburgh outfit this season and have helped them keep five clean sheets.
With the draw, Hibernian are fourth in the Scottish top-flight log with 31 points from 18 matches. They confront Rangers for their next encounter on Wednesday.