After a sudden burst from Scott Murray, Edinburgh came to life and scored a vital try to get back in the game. Edinburgh then took control of the game and at the 20 minute mark were leading 14-7.
It took just 90 seconds after the restart for Edinburgh's John Senio to cross the line and secure the bonus point.
Connacht continued to fight and were rewarded with another try from Dan Riordan and Warwick converting.
Both sides managed to cross the line again scoring tries, both followed with conversions.