Wright’s Bristol City cruised to a thumping 4-0 win over Mooy’s Huddersfield Town at Ashton Gate Stadium on Saturday (AEDT).
In a shock result, City (19th) stunned third-placed Town with goals to Lee Tomlin, Tammy Abraham, Aden Flint and David Cotterill helping the hosts move one point clear of the relegation zone.
Wright and Mooy played the full 90 minutes for their respective sides, with the defender earning the bragging rights as they both head into Socceroos camp this week.
Elsewhere on Saturday, Socceroos flyer Mat Leckie got through a full shift for FC ingolstadt in the Bundesliga but could do little as his side fell to a 1-0 loss away to Borussia Dortmund.
Superstar striker Pierre Emerick Aubameyang netted the only goal of the game as Ingolstadt slipped to their third loss in four games.
Ingolstadt remain second bottom in the Bundesliga and eight points adrift of the relegation play-off place.