Smith top-scored with 70 as Australia, fresh from their 59-run win in the first of a five-match series in Southampton on Thursday, were sent in by England captain Eoin Morgan in awkward overcast conditions for batting.
Together with George Bailey (54), he put on 99 for the second-wicket in a match reduced by rain to 49 overs per side.
Australia's battery of big-hitting all-rounders then came to the fore as 96 runs were scored in the last 10 overs.
Off-spinner Moeen Ali's figures suffered in a return of one for 68 while all-rounder Ben Stokes's three-wicket haul came while the boundary bonanza was at its height.
Australia suffered an early setback when David Warner, who struggled against the short ball during England's 3-2 Ashes series win, was struck a painful blow on the left thumb as he got in a tangle trying to play fast bowler Steven Finn's second-ball bouncer and retired hurt.
Smith, however, seized on anything short, while Bailey, placing the ball well, completed his first ODI fifty since the World Cup.
It was not long before Australia's 141 for two became 171 for three.
Leg-spinner Adil Rashid, who took four for 59 on Thursday, ended Smith's 87-ball knock as the captain, trying to drive a well-flighted ball, sliced to backward point.
Glenn Maxwell (49) got the late run spree going with two sixes and a four off successive balls in an Ali over that cost 19 runs in total.
Shane Watson (39) weighed in with two huge sixes, off consecutive Ali deliveries, the first soaring straight into the top deck of the Lord's Pavilion.
But the four that saw him to his fifty off the paceman almost resulted in a stunning one-handed catch by a leaping Jason Roy at cover-sweeper.
Marsh was eventually caught behind attempting another big hit, off Stokes.