Evan Horwood's first goal since joining from Hartlepool in the summer gave Rovers a half-time advantage but former Kidderminster striker Matt struck twice in 18 minutes to condemn the hosts to defeat at Prenton Park.
Horwood gave Tranmere a 37th-minute lead after his free-kick sailed over Fleetwood's wall and past Scott Davies.
Fleetwood equalised after a mix-up between Owain Fon Williams and Ash Taylor allowed Matt to side-foot home after 48 minutes into an empty net.
Matt then gave the Cod Army the lead after 66 minutes after beating Ian Goodison and Taylor before cooling finishing past Fon Williams.
After Fleetwood's equaliser, Stewart Murdoch could have given Town a 56th-minute lead but he headed Matty Blair's cross wide.
Tranmere went close to equalising late on when Taylor's header was cleared off the line by Steven Schumacher but the League Two side held on.
- Sports & Recreation
- Ash Taylor
- Owain Fon Williams