Warner's 157-ball knock propelled the hosts to a 50-over total of 321-6, a mountain that ultimately proved too high for Sri Lanka despite late half-centuries from Nuwan Kulasekara and Upal Tharanga that threatened a comeback.
The victory on a drizzly night at the Gabba gave Australia a 1-0 lead in the best-of-three final series, with the teams heading to Adelaide on Tuesday for the second final.
Warner belted two sixes and 13 boundaries in his ton, Australia's sixth largest in one-dayers, and teamed up with wicketkeeper Matt Wade for a 136-run opening stand that set up the platform for the win.
Wade was out for 64 attempting to slog over the rope at long-on where Rangana Herath dived backwards to take a spectacular catch with his left hand.
In Image: Australia's David Warner celebrates his century
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