He earned 60 caps for Slovakia, first debuting in 2009, and was included in their squad for the 2010 FIFA World Cup and UEFA Euro 2016.

He won the 2012 FIFA Puskás Award, after he scored a volley from outside the penalty area into the top corner of the goal during a Süper Lig match against Gençlerbirliği.

[1] Stoch's father realized his talent at an early age and placed him with his local club's academy Nitra.

His hard work paid off as he was drafted into Nitra's first team after scoring a hat-trick in an under-17 match, at only 15 years old.

Stoch made his second appearance for the first-team, replacing Mikel John Obi in the 82nd minute of Chelsea's 2–1 comeback win over Stoke City, playing a major part in the lead-up to their second goal.

Stoch joined Turkish team Fenerbahçe on 11 June 2010 on a four-year deal for a fee of €5.5 million.

[16][17] He scored his first goal with the club in the first leg of the Champions League play-off qualifying round against FC Schalke 04.

On 3 July 2014, he signed new contract with Fenerbahçe until 2018 and then joined Al Ain on a one-year loan deal for €1 million.

The main reason for this choice was Slavia's big chance of qualification into the Champions League group stage via upcoming play-off round against APOEL.

[21] On 20 September 2017 after the 5–1 victory against Třinec in MOL Cup Stoch shouted, with Slavia fans, "Smrt Spartě" ("Death to Sparta") and was called before the Czech Football League's Disciplinary Commission.

[24] On 28 June 2019, Stoch was given permission by Slavia to fly to Greece to discuss a potential move to PAOK.

[32] On 17 September 2022 Stoch made his debut for Motorlet Prague in a 3–1 home win against Sokol Hostouň.

[34][35] On 9 October 2014, Stoch scored the game-winning goal in the 2–1 UEFA Euro 2016 qualification win against title-holders Spain three minutes from time.

[36] Stoch became a part of a preliminary EURO 2016 squad and capped in a match against Germany, only days after death of his mother, due to which he had to be excused from a training camp in Austria in the previous week.