The exemplary Williamson struck 12 fours in his 118 before he was caught at mid-off by Mark Wood off David Willey the ball after lofting a sweetly-timed straight six.
Grant Elliott fell for five but by the time Taylor played a ball from Willey on to his stumps for 110 his side needed only 13 off the last 4.1 overs.
Luke Ronchi tried to finish the job in spectacular style by smearing Ben Stokes over the boundary rope but was caught by Jason Roy. It only delayed the inevitable, though, and Tim Southee hit the winning runs with an over to spare.
New Zealand lead the series 2-1 with two matches left.
"300 was certainly well within the game but I think what cost us was Kane and Ross's partnership," England skipper Eoin Morgan said at the presentation ceremony.
"They played really well today and all credit to them."
After the fireworks of the first two matches which produced a combined 1,369 runs, Sunday's clash at the Rose Bowl was a slightly more sedate affair, but gripping nonetheless.
England ultimately paid for failing to bat out their allotted 50 overs and several dropped catches.
Wicketkeeper Jos Buttler allowed Taylor to escape on 67 and the same batsman was dropped by Stokes at short mid-wicket -- both off Wood who himself contrived to fumble a simple chance shortly after Williamson reached his century.
England won the toss and made a steady start before opener Alex Hales nicked one to Southee at second slip to give Ben Wheeler his first international wicket and Roy was bowled by Southee.
Captain Eoin Morgan (71) added 105 for the third wicket with Joe Root (54) but New Zealand's attack never lost control.
Stokes scored 68 from 47 balls and with Sam Billings smashing 34 off 16 balls England looked set for a charge before the wickets started tumbling.
Wheeler ended with three for 63 while Southee was the pick of the bowlers, taking three for 44.
New Zealand lost openers Martin Guptill and Brendon McCullum with less than 40 on the board, but Williamson and Taylor gave a masterclass in calm, measured batting to propel their side towards victory.
(Reporting by Martyn Herman; Editing by Ed Osmond)
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