Murat Tleschew began his career in 1998 in his hometown at the first division side FK Kazakh Taras. From 2003 to 2006, the striker ran on the Irtysh Pavlodar for and won with the club two championship titles. The season 2007 spent at FK Astana. In the next season Tleschew was in the squad of Ordabassy Shymkent. 2008, the striker returned to the Irtysh Pavlodar. In the spring of 2009 he moved to league rivals FK Aktobe, with whom he won the Kazakh Cup for the third time. After two seasons in Aktobe he returned again to Pavlodar.
Tleschew was used eight times in the Kazakh national football team, scoring one goal.
- Kazakh champion: 2003, 2006, 2009
- Kazakh Cup Winners: 2000/ 01
- Kazakh top scorer: 2005, 2008, 2009