Sri Lanka routs India to win Asia Cup
India, chasing 274 runs, was dismissed for 173 in 39.3 overs with Mendis often unplayable in his eight overs.
Sanath Jayasuriya had earlier smashed 125 - his 27th century in one-day internationals - after India won the toss and chose to bowl first.
"I am happy with the way we played," Sri Lankan captain Mahela Jayawardena said. "A lot of people had talked about 300-plus totals in this tournament but we knew if we put 275-280 runs on the board it could be a good score for our spinners to defend."
Mendis' figures were the best ever in the nine Asia Cups, beating Pakistan's paceman Aqib Javed's 5-19 against India in 1995 at Sharjah, United Arab Emirates.
The Indian batsmen were facing the 23-year-old Mendis for the first time in the tournament and had no answer to his masterful bowling.
Mendis came on in the 10th over after hard-hitting Virender Sehwag (60 off 36 balls) had pushed the score to 76-1.
"I needed a wicket as Virender was playing really well," Jayawardena said. "I took gamble on Ajantha because he was the kind of a bowler who could bowl wicket to wicket and it paid off."
Mendis broke through in his second delivery when Sehwag, who had hit 12 boundaries, misread a quick delivery and was stumped. An over later, Mendis clean bowled Yuvraj Singh (0) and Suresh Raina (16) with balls that skidded through the Indian lefthanders before Rohit Sharma was trapped leg before wicket off a pefect off-spinner.
Mendis returned for his second spell and claimed the wickets of Irfan Pathan (2) and R.P. Singh (0) before Chaminda Vaas (2-55) ended captain Mahendra Singh Dhoni's innings - caught behind for 49.
"We thought 273 was chaseable but Mendis was a difficult bowler to pick and his bowling made the difference," Dhoni said. "Mendis bowled brilliantly and we didn't have clues. We couldn't pick up his deliveries."
Earlier, Jayasuriya smashed 125 off 114 balls before India bowled out Sri Lanka in 49.5 overs.
Jayasuriya's innings included nine fours and five sixes. The hard-hitting opener revived Sri Lanka's innings by adding 131 runs for the fifth wicket with Tilakaratne Dilshan, who scored 56.
India hit back in the last 10 overs, conceding just 57 runs with R.P. Singh claiming 3-67.
India, which opted to bowl first, struck through its paceman Ishant Sharma (3-52) before Jayasuriya launched a counterattack.
Sharma's triple strike reduced Sri Lanka to 66-4 after 12 overs, including the key run-out for only four runs of Kumar Sangakkara, who was chasing his fourth century in the tournament.
Sharma had captain Mahela Jayawardena (11) caught at point by Rohit Sharma and then removed Chamara Kapugedera (5) and Chamara Silva (0) in his sixth over.
But Jayasuriya felt little pressure from the wickets falling around him and hit paceman Singh for 26 runs in one over with three sixes and two boundaries.
Jayasuriya went on to complete his first century against India in the last four years off 79 balls.
"Sanath batted well and without his batting we couldn't have put competitive total," Jayawardena said.
With 27 centuries, Jayasuriya is now the second century-maker in one-day internationals behind India's Sachin Tendulkar, who has 42 centuries.
India came back strongly when it removed both Jayasuriya and Dilshan in the space of 21 deliveries. Ishant Sharma took a well judged catch at deep midwicket as Jayasuriya failed to keep down his sweep shot from part-time off-spinner Virender Sehwag.
Dilshan mistimed a pull shot off left-arm paceman Pathan and skied an easy catch to Dhoni behind the wickets after hitting three boundaries in his 74-ball knock. Pathan finished with 2-67.