Hull City raced to a 2-0 lead at the halftime break after dominating the first 45 minutes of the match.
However, Wright's Bristol side delivered an inspired second half showing to snatch a unlikely victory thanks to an 89th minute header from Josh Brownhill.
Irvine, who played the full 90 minutes, was unlucky not to find himself on the score sheet during the opening exchanges when his headed effort missed narrowly.
Goals to Aden Flint, Bobby Reid and Brownhill ensured Wright and Bristol had the last laugh.
The win moves Bristol to fifth in the Championship, while Hull remain in 20th.
Millwall defender James Meredith was on the losing side as he played the full 90 minutes in his team's 1-0 defeat at cross London rivals Fulham.
In the Eredivisie Mark Birighitti's NAC Breda suffered a 2-1 defeat to Heracles with the Aussie shot stopper starting the match.
Feyenoord's Australian goalkeeper Brad Jones had a better result keeping a clean sheet in a 2-0 win against Groningen.
In Austria Jimmy Jeggo played 90 minutes in Sturm Graz's 1-0 win against LASK Linz. Fellow Aussie James Holland was an unused substitute in the same match.
Tommy Oar's APOEL secured an emphatic 6-1 win Olympiakos with the winger putting in an inspired performace.
Oar provided three assists in the emphatic win.
In Scotland Scott McDonald scored in Dundee United's 1-1 draw with Brechin City.