Thirimanne has been the surprise packet of Sri Lanka's tour of Australia, turning himself from an injury reinforcement into last-start match-winner in Adelaide, to bolster hopes of a one-day series upset.
The 23-year-old also scored a fighting 91 after being rushed into the third Test loss at the SCG and is the tourists' form batsman heading into Friday's pivotal ODI in Brisbane.
Vice-captain Mathews felt Thirimanne's unbeaten 102 at the Adelaide Oval, bringing up his maiden international century and the eight-wicket victory with a boundary, highlighted the left-hander's immense potential.
Before his fighting Test top-score in Sydney, Thirimanne had struggled opening in seven previous Tests (averaging just 20) while he'd also failed to nail down a place in the one-day team (26 in 32 matches).
But Mathews said the composed technician was on track to follow in the footsteps of veteran stars Mahela Jayawardene and Kumar Sangakkara.
"He's seen so many challenges," the allrounder said. "He's been batting up and down (the order) and he's stood up for all the challenges and he's taken it in a good spirit and performed.
"He grabbed his opportunity in the Test series and he also showed his mark in the second ODI.
"He's stayed calm in those situations and he handles them really well.
"He's definitely a guy to watch out for the future."
With Jayawardene, 35, standing down as captain at the end of the Australian tour and fellow batsmen Sangakkara, Tillakaratne Dilshan and Thilan Samaraweera all in their mid-30s, Sri Lanka are desperate for the likes of Thirimanne, Dinesh Chandimal and Dimuth Karunaratne to step up.
Mathews, tipped to succeed Jayawardene as skipper, felt the manner of Sunday's victory in Adelaide showed the tourists had finally clicked together Down Under.
There's a renewed confidence following a month in Australian conditions and Mathews believes they can atone for the disappointment of a 3-0 Test whitewash by clinching the one-day series 4-1.
"We have to look forward to winning all three games," he said.
"We have clicked at the right point so it's a good positive for the whole team."