Sangakkara's team-mate Muttiah Muralitharan, who this week overtook retired Australian Shane Warne as the leading wicket-taker, already tops the Test rankings for bowlers, according to the International Cricket Council rankings.
Left-handed Sangakkara, 30, continued his brilliant recent form by making 92 and a match-winning 152 to help Sri Lanka defeat England by 88 runs in the Kandy Test on Wednesday.
His second-innings century made him the first batsman in history to score 150-plus in four consecutive Tests, having scored 200 not out and 222 not out against Bangladesh at home in July and 192 against Australia in Hobart last month.
Australian legend Don Bradman, Wally Hammond of England and Mudassar Nazar of Pakistan did it in three successive Tests.
Sangakkara, with 938 points, overtakes Australian captain Ricky Ponting, who is now in second place with 936 points.
Muralitharan ended the first Test with 713 wickets from 116 matches. The second Test against England starts here on Sunday.
1. Kumar Sangakkara (SRI), 938 points
2. Ricky Ponting (AUS), 936
3. Jacques Kallis (RSA), 935
4. Mohammad Yousuf (PAK), 885
5. Mike Hussey (AUS), 874
6. Kevin Pietersen (ENG), 848
7. Younis Khan (PAK), 816
8. Matthew Hayden (AUS), 803
9. Shivnarine Chanderpaul (WIS), 762
10 Michael Clarke (AUS), 751
1. Muttiah Muralitharan (SRI), 910
2. Makhaya Ntini (RSA), 808
3. Dale Steyn (RSA), 775
4. Stuart Clark (AUS), 769
5. Matthew Hoggard (ENG), 733
6. Brett Lee (AUS), 726
7. Shane Bond (NZL), 724
8. Anil Kumble (IND), 724
9. Shaun Pollock (RSA), 701
10. Shoaib Akhtar (PAK), 701