Corser was also the lead vocalist in a 4-piece cover band called "Sideshow Bob" that played around a few Melbourne pubs during the mid-late 90s (1995-1996) – namely at places like the Royal Hotel in Essendon, Victoria, Australia.

Corser graduated from Deakin University in 1996 with an Honours B.A. in Media Studies. He was lead vocalist in a band called Tender Prey in the early 1990s. They played their majority of gigs at the Shoppingtown Hotel, Doncaster, Victoria, Australia. He was lead vocalist in a band called Stone the Crowes. They played Rolling Stones and Black Crowes covers as well as many original songs. They released "Perfect Face" on a Nu-Music CD in the mid-1990s.

Corser's breakthrough role came in 1998, when he was cast in the leading role (from a field of 6,000) in the Australian production of the musical Rent. Corser portrayed the role of 'Roger', a HIV-positive musician. The show played seasons in Sydney and Melbourne and launched Corser into a successful career in television. His other theatre credits include Leader of the Pack and Below. In 2009 he took to the stage in the theatre production Secret Bridesmaids' Business.

Corser played Detective Senior Constable George Newhouse in the final four episodes of Water Rats in 2001. Corser played Peter Johnson in the Australian drama series McLeod's Daughters from 2001–2004. He played the lead role of Alex in the Australian movie Let Me Not in 2005. He portrayed Photographer Adam Logan in the Australian television series Last Man Standing and Dr Hugh Sullivan in Home and Away from 2006 to 2007. Corser has appeared in numerous television adverts, most notably for car maker Hyundai.

Corser's oldest daughter, Zipporah Mary Corser, was born in 2002 from his previous relationship with singer Christine Anu.

From 2008-2010 Corser starred as Lawson Blake in the Australian police drama Rush, which follows the lives of members of the prestigious Tactical Response team (TR), which is based on the real life Victoria Police Critical Incident Response Team, a highly mobile unit that fills the operational gap between general duties police and the SWAT-like Special Operations Group.

In 2007 Corser married Renae Berry. Berry battled cancer but the couple learnt at Christmas 2009 that they were expecting their first child. On 18 August 2010, the pair welcomed a son named Budd. This was followed by daughter Cilla June Corser in 2012, and another son Dustin Corser in summer 2015.

From 2012 to 2014, Corser starred in the Network Ten 1970s period drama Puberty Blues as philanderer Ferris Hennessy, abusive husband to Yvonne, and father to series protagonist, Gary. He then starred in the Network Ten drama Party Tricks as Victorian Opposition Leader David McLeod alongside Asher Keddie.

In 2013, Corser starred, alongside Rachel Griffiths, in the American television series Camp.

Since 2015, Corser has co-starred as John Doe in the critically acclaimed ABC series Glitch, as well as in the ABC series The Beautiful Lie, a modern adaptation of Anna Karenina, as Xander Ivin.

Since 2016 he has been starring as series protagonist Dr Hugh Knight in the Channel 9 series Doctor Doctor.

He is currently part of the main cast of Glitch in the role of John Doe/William Blackburn and is the series lead of Doctor Doctor. In 2017, he was nominated for the Gold Logie.