The 22-year-old Sri Lanka all-rounder came in at 31 for 4 in the sixth over, when it looked as if Sourav Ganguly's team would fold for a small total.
But after being lucky to survive off the first delivery he faced, he went from strength to strength. He pulled a short delivery from Jaskaran Singh but got a top edge that went over the wicketkeeper for a six and then took charge along with Owais Shah.
Kolkata were only 57 for four after ten overs, but Mathews and Shah repaired the damage, adding 72 runs in 65 balls for the fifth wicket, to take the total to 103 for four after 16 overs.
Mathews showed scant respect for his compatriot Chaminda Vaas as he lofted him straight down the ground for the second six of the over that fetched 18 runs.
He completed his half-century in style, carting T Suman high into the stands at wide long-on.
It took the young Sri Lankan just 38 deliveries to reach his fifty. When the Kolkata side's 20 0vers were completed he was unbeaten on 65 off 46 deliveries, which included five boundaries and four sixes.
He then did well with the ball, claiming the vital wicket of Rohit Sharma. He deceived the Deccan youngster with a slow bouncer and had him caught by mid-off fielder Hodge. He finished with one for 27 in four overs.
The team that finished at the bottom last season will be looking for more from the Sri Lanka in the coming matches.
Kolkata stun Deccan in IPL opener
Injured Mathews to miss rest of ODI series
Spotted: Sourav Ganguly
Sourav Ganguly turns 36
Mohali T20: Sehwag, Yuvraj help India thrash Lanka