In 2008 Behich was signed to the club's first team, surprisingly because the coach; Ian Dobson, had preferred experienced players within his squad, where he made his debut on 22 February 2008 in a 2–0 loss against Richmond.

[18][19][20][21] Behich made his debut for Melbourne Victory's first team on 16 January 2010, in the 2009–10 A-League season, where he was substituted on to the field in the 83rd minute for Carlos Hernández in a 6–2 win against Perth Glory.

[24] He was substituted on during the second half of the 2009–2010 A-League Grand Final when Melbourne lost on penalties to Sydney, and is notable for the narrowest miss of the match, which could have been the winner.

He appeared 5 more times for the side, departing from the club in June, as they finished in second spot of the Victorian Premier League table.

[25][26] By July 2010, he trialled with the Melbourne Heart squad where he took part in a round of warm up matches that the club played, including a 2–0 defeat against Everton.

Behich, shortly after trialling with Melbourne Heart, signed a seven-week deal with the club as an injury replacement player for Kristian Sarkies until October 2010.

Excelsior manager John Lammers spoke of his interest in the exciting youngster to Rotterdam newspapers Algemeen Dagblad and NRC Handelsblad:[29][30] "We are looking to bring Aziz to the club, he's an exceptional talent who we've been watching.

The transfer fee paid to Bursaspor was reported as for $4.5 million[35] On 24 May 2019, it was announced Behich would return to Turkey to join İstanbul Başakşehir for the 2019–20 season, having agreed a three-year deal.

[43] Behich was selected to play against Yemen's under-23 side for the Football at the 2012 Summer Olympics – Men's Asian Qualifiers Preliminary Round 2.

On 14 June 2011, in preparation for the 2012 AFC Men's Pre-Olympic Tournament, Behich featured in a 6–0 win against Singapore under-23 where he scored Australia's sixth goal in the 90th minute.

[48] Behich was called up to the Australian national team by Holger Osieck for a friendly match against South Korea on 14 November 2012, where he made his debut.

[49] He was included in Ange Postecoglou's 2015 AFC Asian Cup-winning squad where he played 2 matches as Australia won the tournament on home soil.

[50] Behich made a run past Argentinian defenders and had a chance at an equalising goal in the dying seconds of the Round of 16 game, but his shot was stopped by Emi Martinez.