The result levels the series following England's defeat on Sunday, going into the decisive final match in Auckland on Saturday.
England's bowlers, particularly James Anderson, had done a superb job to dismiss New Zealand for 269 in 48.5 overs at a small venue with short square boundaries, where a score of at least 300 was needed to set a competitive total.
Joe Root (79 not out) then picked up from where Cook left off when the captain was dismissed by Tim Southee, while Jonathan Trott finished on 65 not out as England easily chased down the total for the loss of two wickets in 47.4 overs.
Taylor, who was dumped as captain by coach Mike Hesson in December and chose not to tour South Africa, had barely played any cricket since and had looked rusty in his return to the international scene.
The 28-year-old took a little time to get into his stride and also curbed his attacking instincts to anchor the innings after England's opening bowlers Anderson and Steve Finn had put the hosts under immense pressure.
Taylor combined with Kane Williamson (33) in a 72-run partnership, then 52 runs with Grant Elliott (23) for the fourth wicket before the latter was dismissed by Finn in the first over of the batting powerplay to leave New Zealand struggling at 143-4 in the 36th over.
McCullum, however, then thrashed nine fours and four sixes in a 44-minute knock that included a 100-run partnership with Taylor, 77 of which came in 5.5 overs.
McCullum's dismissal then sparked a collapse with the final five wickets falling for 26 runs as Anderson returned to mop up the tail and finished with impressive figures of five for 34.
The anti-climax gave England hope of a a successful chase - something confirmed after Cook and Ian Bell's 89-run opening stand in 20 overs.
Bell had mixed good with bad, assured timing interspersed with air shots as the new ball swung for New Zealand's pace bowlers.
But it was a switch to the spinners which brought the hosts a breakthrough, Bell getting underneath a sweep at Williamson to be caught on the square-leg boundary.Cook still appeared to be carrying the game, as he and Trott put on another 60.
But the captain could not convert a 67-ball 50 into three figures, tamely chipping a full toss straight back to Tim Southee.
Trott and Root found boundaries hard to come by initially but placed the ball and scurried well in an unbroken century partnership which always kept the equation in England's favour - all the more so after the young Yorkshireman was badly dropped on 25 by McCullum racing back to a mishook off Trent Boult when 75 were still needed at seven-an-over.
Root then kicked on as required past his half-century in just 38 balls, allowing Trott to remain in his accustomed anchor role.
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