Kislyak scored from a rebound in the 33rd minute after Vladislav Stoyanov failed to block Dmitri Verkhovtsov's shot from inside the box.
Belarus attacked from the start and was in control of the game.
Timofei Kalachev had the first chance for the home side nine minutes into the game but his shot hit the crossbar. Andrei Voronkov thought he had scored from the rebound but the goal was disallowed for offside.
In a stunning save, Stoyanov jumped to palm over Aleksandr Martynovich's shot in the 40th.
Belarus continued to dominate possession in the second half, with Kalachev hitting the crossbar in injury time and then firing the rebound right into Stoyanov's hands.
Belarus is second to France in Group D in qualifying for the next year's European Championship. The team will play two back-to-back matches against Bosnia in September.
Bulgaria has five points from as many games in Group G.
Belarus: Yuri Zhevnov, Aleksandr Kulchiy (Stanislav Dragun, 46), Aleksandr Martynovich, Sergei Kislyak, Timofei Kalachev (Pavel Sitko, 90), Aleksandr Yurevich (Pavel Nekhaichik, 46), Vitali Trubilo, Andrei Voronkov (Sergey Kornilenko, 56), Anton Putilo, Dmitri Verkhovtsov (Egor Filipenko, 83), Igor Shitov (Maksim Zhavnerchik, 46).
Bulgaria: Vladislav Stoyanov, Ivan Ivanov, Nikolay Bodurov, Ivan Bandalovski (Kostadin Stoyanov, 76), Petar Zanev (Boris Galchev, 46), Chandar Yankov (Apostol Popov, 83), Blagoy Georgiev, Marcos Marquinhos (Nikolay Dimitrov, 66), Spas Delev (Stanislav Manolev, 46), Ivan Stoyanov (Zhivko Milanov, 46), Ivelin Popov.