Australia looked set for a total in excess of 350 while Warner and captain Aaron Finch (82) were at the crease, but Mohammad Amir (5/30) staged a grand comeback with his best ODI bowling figures to bowl their opponents out for 307.
Pakistan's innings ended at 266 in 45.4 overs but not before the duo of Sarfaraz Ahmed and Wahab Riaz gave the Australians a scare with a rearguard action that revived their hopes for a while.
Pakistan were at one stage tottering at 160 for six in the 30th over.
Riaz smashed 45 off 39 balls with two fours and three sixes, while Sarfaraz made 40 off 48. The side's top-scorer though was opener Imam-ul-Haq (53), Mohammad Hafeez contributed 46 while Hasan Ali blazed away to 32 off only 15 balls before Mitchell Starc closed out the game at the death.
Earlier, sent into bat after the coin landed in Pakistan skipper Sarfaraz Ahmed's favour, Australia were off to a steady start with Warner and Finch helping them to 50 in 10 overs.
Amir started with a maiden and going with only four mainline bowlers, Australia knew they needed to score big to put Pakistan under pressure.
The Aussies broke free against Shaheen Afridi, with Finch hitting him over the deep square leg fence for a six and Warner employing the pull shot to get a four. As Australia looked for quick runs, Amir showed his class by bowling another maiden over.
Apart from the singles and twos, both managed to find the ropes occasionally, before Finch carted Mohammad Hafeez for 16 runs with the help of a six and two boundaries.
After a stand that yielded 146 runs in 22.1 overs, Amir provided Pakistan the much-needed breakthrough when he had Finch hitting one high up in the air towards extra cover.
Sitting pretty at 189 for two in the 29th over, Smith tried to up the ante but in doing so, ended up giving a catch to Asif Ali, who had dropped a sitter in the slips earlier at The Cooper Associates County Ground.
Glenn Maxwell struck 20 in 10 balls even as Warner reached the three-figure mark when an edge flew between the keeper and the wide slip for a four. He got out shortly after celebrating his century with gusto.