2012 Barton won his first
ITF Futures title defeating
Samuel Groth in the final 7–6(3) 6–3. Barton played the
2013 Australian Open Wildcard Playoff defeating
Thanasi Kokkinakis and
Nick Kyrgios.
2013 Barton defeated Croatian
Ivo Karlović 6–7(0) 7–6(5) 7–6(5) at the
Apia International Sydney qualification, Then beat
Tatsuma Ito 7–5 6–1. Before losing to
Björn Phau of Germany. Barton reached the 2nd round of the
Australian Open with
John Millman defeating
Marinko Matosevic and
Daniel Gimeno Traver in the opening round. Before losing to
Kevin Anderson and
Jonathan Erlich. Barton won his first
ATP Challenger Tour Title in
West Lakes defeating the number 2 British player
James Ward in the final 6–2 6–3. Barton lost round 1 of qualification at the
French Open,
Wimbledon and lost to
Donald Young at the
US Open. He ended 2013 with a ranking of 253.
2014 Barton lost in round 1 of qualification at the
2014 Brisbane International,
2014 Apia International Sydney and
2014 Australian Open in January, before returning to the Challenger and Futures circuit in Australia and Croatia. He ended 2014 with a ranking of 524.
2015 Barton played Challengers and Futures in 2015, making three finals and winning two of them. He ended 2015 with a ranking of 299.
2016 Barton commenced 2016 by qualifying for the
Auckland ASB Classic defeating
Denis Kudla 6–2 6–0. In the main draw he beat
Steve Johnson first round 6–3 3–6 6–3, this was his first ever ATP Tour level win. He then lost second round to top seed and world number 6
David Ferrer in straight sets. Barton qualified for Houston defeating
Reilly Opelka in straight sets. He defeated
Frances Tiafoe in the opening round before losing to defending champion
Jack Sock second round. At
Roland Garros he lost in qualifying to
Radek Štěpánek 6–3 2–6 5–7. In June, Barton went on to qualify for his first main draw grand slam event at
2016 Wimbledon Championships, defeating
Karen Khachanov in the final round of qualifying 7–6(1) 6–7(1) 6–2 6–3. In the main draw, Barton recorded his first ever grand slam victory over Frenchman
Albano Olivetti in 5 sets 6–7(7) 7–6(5) 6–3 6–7(5) 14–12. Barton was defeated by
John Isner second round 6–7(8) 6–7(3) 6–7(8). Barton defeated
Nikoloz Basilashvili at the
2016 US Open qualifying 6–7(3) 6–2 7–6(6). Barton ended 2016 with a ranking of 197.
2017 In January, Barton qualified for the 2017 Apia International Sydney by defeating
Mikhail Kukushkin. He upset
Kyle Edmund in the opening round on centre court 7–6(3) 7–6(5). Before losing to eventual champion
Gilles Müller in the second round 1–6 6–3 4–6. ==Professional career finals==