Boult exploited helpful bowling conditions by snaring Jonny Bairstow, Joe Root and Ben Stokes to leave England, seeking to level the series after a heavy defeat in Cardiff, reeling on eight for three.
England then lurched to 55 for five but Livingstone’s majestic counter-attack, clubbing nine fours and one six, helped the hosts to 226 for seven in a contest reduced to 34 overs per side because of rain.
The big-hitting all-rounder, whose ODI best was the first time he batted 50 or more balls in an England innings, shared a stand of 112 in 77 balls with Sam Curran – who returned to the XI alongside Bairstow and Moeen Ali – in this second of four World Cup warm-ups.
Jason Roy’s back spasm meant he once again missed out while Adil Rashid, who struggled with cramp at Sophia Gardens, missed out although England insist they are merely taking a precaution over the pair with the World Cup in India just three and a half weeks away.
After England were asked to bat first, Boult wreaked havoc in his second over, squaring up Bairstow, whose squirted leading edge might have landed safely on another day but a leaping Mitch Santner took a superb one-handed catch at cover.
Root was lbw second ball, eschewing a review as replays showed a delivery swinging back in would have clattered leg stump, with the Yorkshireman out for his fourth duck in his last 10 ODI knocks.
After a double wicket maiden, Boult had his third in the space of eight balls after an advancing Stokes backed away and clothed to mid-off while Harry Brook spooned Matt Henry to a backpedalling mid-on, with England’s top four mustering just nine runs between them in 32 deliveries.
Jos Buttler sought to upset Boult’s rhythm and though he mistimed a couple of drives, the tactic worked as a more convincing stroke brought up a third four in an over which yielded 15 runs.
Buttler’s eyes lit up at a rare Santner long hop but was on the shot too early and, perhaps undone by the ball sticking in the surface, dragged on to his leg stump, having made 30 of England’s 55 for five.
Moeen Ali drove Henry then Tim Southee lustily through the covers as he rebuilt alongside Livingstone, who settled into his stride by rocking back and cutting Southee away for four.
Livingstone was strong all around the wicket while Moeen slog swept Rachin Ravindra for six before clipping Southee wide of Tom Latham for four to bring up England’s 100. But from the next ball, Moeen was cramped for room and aimed an ungainly slash for Glenn Phillips to take a fine low catch.
Livingstone flayed three fours in a Southee over as he brought up a second successive fifty in 47 balls while he was ably supported by Curran, who launched Santner over cow corner for six.
Livingstone took his four count against Southee to six with back-to-back boundaries – an unconvincing mow before a more authoritative drive – before hammering Henry into the stands for his lone six.
Curran departed for 42 off 35 balls in the last over while Willey thumped his first ball for six but Livingstone, despite facing the last two balls, was left stranded five adrift of a maiden ODI ton.