Pakistan were reduced to 19-2 by the sixth over before a partial recovery helped the tourists move to 59-3 by lunch on the opening day.
Prasad, working up a tidy pace on a pitch that afforded bounce and movement, bowled Ahmed Shehzad off the inside edge with his third delivery after being hit for a boundary off the first.
The seamer then trapped Khurram Manzoor leg-before in his third over, but Azhar Ali and Younis Khan settled in to put on 37 as the wicket eased out under the mild sun.
Ali, who hit five boundaries in his fluent 30, failed to last till lunch as he fell to a good delivery from left-arm spinner Rangana Herath, which turned and clipped the off-stump.
At the break, Younis Khan was unbeaten on 21 and skipper Misbah-ul Haq had yet to score.
The start was delayed by 30 minutes due to a wet outfield caused by overnight rain. Bad weather has been forecast on all five days of the Test.
Both teams went in with two spinners -- Saeed Ajmal and Abdur Rehman for Pakistan, and Herath and Dilruwan Perera for the hosts -- hoping the grassless pitch provides some turn later in the match.
Former Sri Lankan captain Mahela Jayawardene, who is retiring from the longer format after the two-Test series, walked out to field amid bursting firecrackers as school children gave him a guard of honour with raised bats.
Giant posters of the batsman, who is sixth in the all-time scorers' list with 11,671 runs in 147 Tests, adorned the Galle International Stadium where some 2,000 home fans were present.