Trailing 2-0 after a pair of abject batting performances in the first two games of the series, Allen's 83 and Phillips's 69 from just 34 balls saw the Black Caps set Jos Buttler's side a daunting target of 203 in the Edgbaston sunshine.
Despite a rapid 40 from Buttler himself, England's chase never got going, Dawid Malan's turgid two from 11 balls in the powerplay a notable lowlight with a view to World Cup selection as the hosts were bowled out for 128 with nine balls to spare.
New Zealand have the chance to level the four-match series in Nottingham on Tuesday before attentions turn to the One-Day International leg, which starts in Cardiff at the back end of the week.
That series acts as England's most important preparation for their World Cup defence in the autumn and having this morning added seamer Brydon Carse to their bowling options, the calls for Buttler and Matthew Mott to keep in-form batter Harry Brook on as well will only grow louder after Malan's failure here.
Heading into this contest, no New Zealand player had yet passed fifty in the series, nor as a collective had they reached three figures better than six-down. Here, though, the platform was more efficiently laid, Devon Conway's hesitancy and run-out by Moeen Ali from the deep the sole early blunder, though Allen would have been gone, too, on 26 had Malan not missed the stumps with his diving underarm.
Tim Seifert was also let off the hook when Will Jacks parried a catch into the fence that ought really have been left to Chris Jordan's renowned hand-eye, the 34-year-old brought into the side as one of two changes, along with Luke Wood, as Sam Curran and Carse were afforded a Sunday afternoon's rest. That mistake did not prove overly costly, Seifert falling soon after for 19 as Liam Livingstone found some sharp turn and Buttler was sharper still behind the stumps.
Allen, though, was beginning to charge. The opener reached his half-century from 35 balls and then kicked on, launching Adil Rashid for three successive sixes - over extra cover, cow corner and then finally the bowler's head - before eventually losing his off-stump to Wood.
Phillips picked up the baton on what turned into a torrid afternoon for England's spin attack - or at least the two-thirds of it to whom Buttler dared throw the ball. Moeen was conspicuous by his absence, the vice-captain's off-spin held back as New Zealand's right-handers overstayed their welcome, but that left Livingstone to bowl the 18th over against a set Phillips, who tucked in, adding three maximums of his own to complete the all-rounders ugly figures of one-for-55.
Less than 48 hours on from his superb debut, Gus Atkinson at least impressed at the death once more, finally ending Phillips stay with a crafty slower ball yorker, before picking up a cheaper second wicket as Daryl Mitchell feathered behind trying to scoop.
The reply began with a pair of frustrating cameos, first from Will Jacks, who again looked in good touch from the off but failed to go on after twice finding the boundary, and then, more troublingly, from Malan.
Though he is by no means the only player who could make way for Brook from England's provisional 15-man World Cup squad, the veteran, who turned 36 on Sunday, is under particular pressure and followed a four-ball duck at Old Trafford with a miserable innings here that doomed England's already uphill chase with its failure to take advantage of the powerplay.
Brook duly helped his first ball fine for four to emphasise the contrast, but on this occasion there was no score of note to further his case either, the 24-year-old successfully overturning a leg-before decision, only to fall for nine skying Ish Sodhi's next ball as the hosts reached halfway still 136 runs short.
So far behind the rate, England's middle-order had little option but to hit out. Buttler took just 21 balls for his 40 but fell caught-and-bowled to Mitch Santner, while Moeen offered his home crowd brief entertainment with some hefty blows in his 26 but could not make a sizeable dent in the total.