Electing to bat first, Sri Lanka lost Kusal Perera for a duck in the second over, just before rain interrupted the match, which was shortened to 35 overs per side at Mahinda Rajapaksa Stadium.
Sangakkara made 63 off 62 deliveries after Sri Lanka was reduced to 31-3. With his second half-century of the series, he and captain Angelo Mathews, 37, added 87 for the fourth wicket.
Thirimanne upped the run rate in the death overs with 62 off 47 deliveries, as 62 runs were plundered off the last five overs. It was his third half-century in his last five ODIs.