The left-handed pair put on 70 for the second wicket as Sri Lanka, sent in to bat by Pakistan captain Misbah-ul Haq, recovered from an early setback to end the morning session at 85 for one in 26 overs.
Karunaratne was unbeaten on 34 and Tharanga, who replaced Kumar Sangakkara for the match, was on 39 at the break. Both batsmen hit five boundaries each.
Pakistan won the first Test in Galle by 10 wickets and Sri Lanka responded with a seven-wicket victory in the second match in Colombo.
Silva made nine when he was caught behind off left-arm seamer Rahat Ali, who was picked alongside Ehsan Ali and Imran Khan in a new-look pace attack by the tourists.
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As the early moisture on the pitch dried out under a hot sun, conditions became favourable for batsmen on the evenly paced wicket.
Rahat proved the most expensive of the four bowlers used by Pakistan, conceding 41 runs in his nine overs.
Both sides reshuffled their packs with four changes each in a bid to break the 1-1 series deadlock.
Two of those changes were forced as pace spearhead Wahab Riaz was sidelined with a fractured hand, and Mohammad Hafeez was not available since he has to be tested after being reported for a suspect action in the first Test.
Left-arm seamer Junaid Khan and spinner Zulfiqar Babar were dropped.
With Sangakkara opting out of the decider and batsman Kithuruwan Vithanage showing poor form, Sri Lanka recalled two left-handers in Tharanga and 34-year-old Jehan Mubarak.
Mubarak played the last of his 10 Tests in December, 2007 -- before any of his current teammates had made their debut.