Engels began his career with SV Allner-Bödingen and later played for TuS Mondorf before moving to 1. FC Köln's academy in 2008.[2] In 2012, he was promoted to the second team's squad, competing in Regionalliga West.[3] On 5 May 2012, he made his senior debut against SV Elversberg, replacing Lucas Musculus in the 74th minute of a 2–1 away loss.[4] One year later, on 13 May 2013, during a resounding 9–0 victory against MSV Duisburg II, he scored his first goal.[5]
In August 2016, Engels joined Polish Ekstraklasa club Śląsk Wrocław.[10][11] In July 2017, he moved to Dutch Eredivisie club Roda JC, suffering relegation with the club at the end of the season.[12][13] In the second division, Engels emerged as his team's top goalscorer, netting 24 goals and securing the second spot on the league's top goalscorers' list, but the team could not secure promotion in the end.[14]
His impressive performance caught the attention of 2. Bundesliga club SV Sandhausen, who secured his services ahead of the 2019–20 season, providing him with a two-year contract.[15]
On 4 October 2020, Engels returned to the Netherlands, signing a two-year contract with Sparta Rotterdam.[16]
On 7 December 2022, it was officially announced that Engels would join Japanese J2 League side Tokyo Verdy for the 2023 season.[17]
On 19 July 2023, Engels returned to the Netherlands for a second time and signed a two-year deal with recently promoted Eredivisie club Heracles Almelo.[18]
^"マリオエンゲルス選手 完全移籍加入のお知らせ" [Announcement of Mario Engels' full transfer]. Tokyo Verdy (in Japanese). 7 December 2022. Archived from the original on 20 July 2023. Retrieved 1 September 2023.