The off-spinner became the first Sri Lankan player to score a fifty and claim 10 wickets in the same match as the hosts clinched their first test series victory over Australia since 1999.
Perera also became the fastest Sri Lankan to claim 50 test wickets, achieving the feat in his 11th match, and won the man-of-the-match award for his all-round brilliance.
"Not too many teams do this to the number-one team," home captain Angelo Mathews said after his team prevailed in the bowler-dominated contest that saw 33 wickets tumble on the first two days.
"After winning the toss, we had to put a decent score on the board and once again it was a special effort by Kusal Mendis and what a performance Dilruwan came up with," he said.
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Resuming day three on 25 for three, Australia captain Steve Smith (30) and deputy David Warner (41) showed positive intent, frequently using their feet against the spinners even though they were merely delaying a defeat that looked inevitable.
Perera separated them when he trapped Warner leg-before with a straight delivery. The batsman reviewed the decision but could not get it overturned.
The spinner then returned to induce Smith into giving a bat-pad catch to Kausal Silva at forward short leg and went on to complete his five-wicket haul when Adam Voges (28) attempted a reverse sweep only to have his leg stump pegged back.
Mendis displayed tremendous reflexes as he stopped a Peter Nevill shot at forward short leg and flicked it back on the stumps to run out the batsman and trigger wild celebrations at the Galle International Stadium.
Sri Lankan spinners claimed 18 of the 20 Australian wickets to fall in the contest, underlying the tourists' struggle on turning tracks.
"It's incredibly hard to play against (spin), particularly (coming) from Australia. We are not accustomed to that. It's very foreign," Smith admitted.
"Our record shows that we've won a game in about 15 or 16 in the sub-continent. We certainly have a lot of work to do. We have to find ways to score and find ways to take wickets and keep the runs dry," added the Australia captain.
Among the visitors, only paceman Mitchell Starc redeemed himself with a match haul of 11 wickets on a spin-friendly track, while none of the Australian batsmen managed a fifty.
The teams now move to Colombo for the third and final test from next Saturday.
(Reporting by Amlan Chakraborty in New Delhi; Editing by Clare Fallon)
