Sangakkara hit his 34th ton during the first day's play of the second Test between Sri Lanka and Bangladesh. This was Sangakkara's 122th Test and 208th innings.
The left-handed number three batsman is the first from the Island nation to score 34 Test hundreds. Mahela Jayawardene is second with 33.
Former captain and India opener Gavaskar played in 125 Tests while Lara featured in 131 for West Indies.
The list for most centuries in Tests is headed by Indian legend Sachin Tendulkar with 51. He retired from international cricket in November last year.
The 36-year-old Sangakkara is joint fifth in the all-time list.
Most Test centuries
Sachin Tendulkar 51
Jacques Kallis 45
Ricky Ponting 41
Rahul Dravid 36
Kumar Sangakkara, Sunil Gavaskar, Brian Lara 34
Mahela Jayawardene 33