The pair put on 93 runs for the second wicket as the hosts carried their lunch score of 40-1 to 123 without further loss by tea on the scheduled second day at the Galle International Stadium.
Silva was unbeaten on 52 and Sangakkara was on 41 after Pakistan captain Misbah-ul Haq surprisingly elected to field first on an easy-paced pitch after winning the toss.
Left-handed Sangakkara, Test cricket's current leading run-getter who is expected to retire during the home series against India in August, has so far hit two boundaries and a six.
Silva, looking comfortable against both pace and spin, has eight boundaries to his name in his eighth Test half-century.
After inclement weather had washed out the entire first day's play on Wednesday, the match began two hours late on the second day due to a wet outfield at the Galle International Stadium.
Left-handed Dimuth Karunaratne scored 21 in an opening stand of 30 with Silva when he was dismissed by left-arm seamer Wahab Riaz in the 13th over of the innings.
Wahab had Karunaratne caught in the slips off a no-ball in his first over before umpire Paul Reiffel warned the bowler for running on the wicket on his follow through later in the same over.
The prolific Sangakkara, who took a break from his English county commitments with Surrey to play for his nation, began ominously by driving his first delivery from Wahab to the mid-on fence.
Rain has been forecast in the southern coastal town for all five days of the match.