Shot-making was not easy on the drop-in pitch at Sydney's Olympic Stadium but Warner blasted an unbeaten 62-ball 90 in a brilliant display of controlled aggression to power Australia to 137 for three wickets.
Kushal Perera (33) and captain Angelo Mathews (35 not out) shone with the bat for Sri Lanka before Thisara Perera (19 not out) clobbered back-to-back sixes to see the visitors home with seven balls to spare.
Melbourne hosts the second and final match on Monday.
Australia were reeling at 53-3 in nine overs after opting to bat first on a tricky surface before Warner added 84 runs in 11 overs with Adam Voges (25 not out) to give the bowlers a decent total to defend.
The hosts lost opener Aaron Finch (one) in the second over when Kushal Perera took a diving catch at short cover after Nuwan Kulasekara had induced a thick leading edge.
Shaun Marsh (six) was sent back by Tillakaratne Dilshan's direct throw while Australia captain George Bailey (11) did not last long either, leaving the onus on Warner to put up a fighting total.
Warner hit Kulasekara for a boundary to bring up his fifty before hitting Mathews for a four and a six in an eventful over in which Kulasekara dropped him at mid-wicket when the batsman was on 69.
In contrast, Sri Lanka were off to a flying start with openers Kushal Perera and Dilshan (16) adding 46 runs before departing in successive overs.
Dilshan was soon in his elements, bending down to play that audacious scoop shot off Mitchell Starc that sailed over the wicket-keeper's head for a six.
Two overs after playing the "Dilscoop", the right-hander sustained a nasty cut over his right eye but batted on with a bandaged eyebrow until Ben Laughlin ran backwards to take a spectacular diving catch and send him back.
Glen Maxwell removed Kushal Perera and Dinesh Chandimal to trigger a mid-innings collapse but Mathews stayed put while Thisara Perera struck successive sixes off Laughlin to score the winning runs.
- Sports & Recreation
- Thisara Perera
- Angelo Mathews
- Nuwan Kulasekara
- Tillakaratne Dilshan