Upul Tharanga ended the match with a boundary struck over cover to remain unbeaten on 67 scored off 59 balls with 12 fours. Kumar Sangakkara was 27 not out.
This was Sri Lanka's second win out of three matches in Group A, while Kenya slumped to their third successive defeat.
In Image: Sri Lanka's captain Kumar Sangakkara, right, and batsman Upul Tharanga celebrate after winning the ICC Cricket World Cup match against Kenya
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