Mahela and Prasanna, who came together on Wednesday, went past the 346-run stand that was put together by Australian great Don Bradman and Jack Fingleton against England in Melbourne in 1937.
The Sri Lankans' stand was broken after Mahela (275), who completed his double ton on Wednesday, was dismissed by Amit Mishra while trying to loft the leg-spinner over cover only to have his stumps rattled.
Before going back to the pavillion, Mahela also completed 9000 runs in Test cricket to become the ninth highest run-getter in this format.