Owens attended Ysgol Gyfun Gymraeg Bro Myrddin, and is a fluent Welsh speaker. He began his career at Carmarthen Athletic RFC before moving to UWIC RFC when he began studying at the university in 2005.

In May 2010, before he had received his first international cap for Wales, Owens was called up to the Barbarians squad, his first match coming against England. This experience helped him score the Magners League 2009–10 try of the season for the Scarlets and improving his line-out throwing statistics.

On 15 February 2010, Owens was called up to the Wales squad for the 2010 Six Nations due to injury to hookers Matthew Rees and Gareth Williams. In June 2011, he was called up to Wales’ 45-man training squad for the 2011 Rugby World Cup, following injury to Richard Hibbard. He made his debut for Wales in their third pool match at the tournament on 26 September 2011, coming on as a second-half replacement in an 81–7 win over Namibia.

In the 2012 Six Nations, Owens was involved in all five games as Wales claimed the Grand Slam.

On 11 March 2013, Owens signed his third professional contract and committed himself to the Scarlets for a further two years.

Owens’ 50th test was a 20–18 loss to France in the 2017 Six Nations Championship, in which he played the entire game, including the 20 minutes of injury time at the end of the second half. Owens was subsequently selected for the British and Irish Lions’ tour to New Zealand. Owens played six matches on the tour, captaining the side in their 22–16 defeat to the Blues in Auckland, and coming off the bench in two of the three test matches against New Zealand. He played 13 minutes of the first test, a 30–15 loss, and 11 minutes of the third test, in which he was penalised for being accidentally offside in the dying minutes; referee Romain Poite originally awarded a penalty that would have given the All Blacks the chance to win the game, but he overturned his decision on review and awarded a scrum instead, and both the match and the series finished as draws.

On 5 January 2019, Owens was selected to play at Number 8 against Dragons as injury cover.

On 5 August 2019, Owens was inducted into the Gorsedd of Bards at the National Eisteddfod of Wales in Llanrwst. He will use the name “Cen y Siryf” (English: Ken the Sheriff), in reference to his nickname.