Bell, who would not have been in the side had England kept faith with Alastair Cook, turned in a classy innings of 187 in 145 balls that looked to put his side on course for a mammoth victory.
Their total of 391 for six equalled England’s high watermark set in 2005 against Bangladesh, though that came in a one-day international rather than a tour match, with Bell’s superb 145-ball stay providing the superb backbone.
But Maxwell, the flashy all-rounder who goes by the nickname ‘The Big Show’, gave watching PM Tony Abbott plenty to smile about with a boundary-strewn century in reply.
The 26-year-old bludgeoned 136 in just 91 deliveries to bring a fanciful chase briefly into the realms of realism.
England can expect to see more of him in Sydney on Friday when the Carlton Mid Tri-Series gets under way.
Both Bell and Maxwell hit 20 fours on a benign Manuka Oval surface, with the Englishman outscoring his rival three sixes to two.
Bell’s late flourish took him clear of the 167 Robin Smith scored against Australia 15 years ago, though that remains England’s top ODI score, and surely inked his name into the World Cup XI.
England will also have been pleased with Moeen Ali and James Taylor, who each contributed 71, though they will be eager to have James Anderson back after the rested seamer was much missed in the field.
Having opted to bat first, both Bell and Moeen had shaky starts.
Pat Cummins, Australia’s World Cup tyro, hurried Bell in the first over only for a loose chip to fall short of mid-on.
Bell responded with an imperious cover drive at Cummins’ next visit and that was as good as it got for the 21-year-old, who shipped 52 in six overs.
Moeen came even closer to an early exit, turning Jason Behrendorff to short mid-wicket, where Maxwell failed to gather a one-handed chance.
From there on Moeen threw caution to the wind, taking full advantage of the fielding restrictions as he struck six boundaries off nine balls from Behrendorff and Simon Mackin.
He had 50 from 29 balls and raced to 71 before holing out to a Maxwell full-toss.
Bell had been content with a supporting role and his second-wicket stand with Taylor was as low-key as it was clinical.
The pair added 141 at almost a run-a-ball, accumulating with minimal risk but complete control.
Bell offered a half-chance on 68 but it would have taken a superb grass-level grab from Maxwell to end his charge.
England were sitting pretty at 201 for one after 30 overs, with Bell easing to his own hundred in 102 balls.
The landmark inspired Bell to kick on and his next 43 balls at the crease contained 12 more fours and three sixes, before he picked out Chris Rogers with a single delivery remaining.
Taylor had already fallen for a disciplined 71, with Joe Root’s 13 and Jos Buttler’s lively 25 tipping the score towards 400.
The PM’s XI appeared to be playing for little more than pride, especially when Woakes removed Cameron Bancroft and Rogers was brilliantly caught off Jordan by the sprinting Buttler.
But Maxwell is a formidable striker and set about leaving his mark on the old enemy.
He lined up the wayward Chris Jordan with three fours and an audacious six over cover in a single over, powering him to 50 in 32 balls.
Ravi Bopara was also to Maxwell’s liking and he was equally productive against the spin of Moeen and James Tredwell.
Maxwell had 97 to his name when he clobbered Bopara for six over long-on, making his hundred in 35 balls fewer than Bell.
The batting powerplay, taken in the 28th over, seemed the decisive moment.
When Maxwell took three successive fours off the returning Stuart Broad, England looked bereft, but the seamer fought back with two dots before having the dangerman held at gully by Taylor.
The chance of an upset went with Maxwell as a relieved England turned 216 for four into 331 all out.
Broad claimed Cummins and Behrendorff in the space of two balls and added took out last man Simon Mackin to finish with four for 40.