Tendulkar, the world's leading Test and one-day scorer, made 138 off 133 balls as India piled up 319-5 after batting first in the day-night match at the Premadasa stadium.
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Sri Lanka made a gallant chase after the stiff target, buoyed by a blistering opening stand of 64 in 7.5 overs by Tillakaratne Dilshan and Sanath Jayasuriya, before they were all out for 273.
Dilshan hit 42 off 29 balls when his dismissal in the eighth over, bowled by Harbhajan Singh, triggered a dramatic collapse in which five wickets fell for the addition of 67 runs.
Off-spinner Harbhajan finished with 5-56 to signal India's morale-boosting win ahead of the eight-nation Champions Trophy which opens in South Africa on September 22.
Skipper Kumar Sangakkara and Thilina Kandamby revived Sri Lanka with a 51-run stand for the sixth wicket, when India earned a lucky break to make it 182-6.
Sangakkara, who made 33, saw his bat fly out of his hands and break the stumps as he attempted to pull a full toss from Rudra P