Ronchi finished unbeaten on 170, with his maiden ODI century coming from just 99 balls, including 14 fours and nine sixes.
Elliott – who was somewhat of a surprise inclusion for the New Zealand World Cup squad – made a somewhat more sedate 104 not out from 96 deliveries as the hosts posted 360-5 from their 50 overs.
Tillakaratne Dilshan (116) scored a hundred of his own in response, his 20th in ODI cricket, but the tourists fell well short of their target and now trail 3-1 in the series with two left to play.
New Zealand’s innings had begun inauspiciously as on a green-tinged, seaming wicket, as Martin Guptill fell first ball edging behind to Kumar Sangakkara off Nuwan Kulasekara.
The rest of the top-order soon followed as the home side fell to 82-4, with the dangerous Brendon McCullum (25), Kane Williamson (26) and Ross Taylor (20) all failing to capitalise on good starts.
But Corey Anderson???s dismissal in the 20th over, lbw to Lahiru Thirimanne for eight, brought Ronchi to the crease and signalled the start of the record-breaking stand.
Ronchi raced to 50 from 38 balls and to his hundred from 74 balls and his final 70 runs coming even more impressively off just 29 balls.
Sri Lanka???s attack were flayed to all parts but it was Suranga Lakmal who suffered the most, with 93 runs coming from his 10 wicketless overs.
He and Elliott scored 122 runs in the final 10 overs as they surpassed the previous 218-run record that Mahela Jaywardene and MS Dhoni made for an Asian XI against an African XI in 2007.
In reply, Dilshan put on 93 for the opening wicket with Thirimanne (45) and another 70 for the third with Jayawardene (30) after Sangakkara (9) fell cheaply.
But when Jayawardene fell, bowled by the impressive Trent Boult (4-44) Sri Lanka – still needing 150 with under 15 overs remaining – collapsed.
Dilshan departed the very next over, scooping one to Nathan McCullum at extra cover off Mitchell McClenaghan, before their final six wickets fell for 28 runs.
It comes after the same six wickets fell for just 31 runs in the fourth ODI in Nelson on Tuesday, and is something Sri Lanka must address if they are to have any hope of getting back in the series.