Vincent made 76, Taylor 71 before Oram blitzkreig as the Kiwis passed 300 against England for the first time on a perfect batting pitch at the WACA in Perth.
Paceman Liam Plunkett captured three wickets at a cost of 54 runs from nine overs while left-arm spinner Monty Panesar was England's most inexpensive bowler, finishing with 2-35 from his full compliment of 10 overs.
But the pair were unable to prevent the Kiwis piling on a massive total, eclipsing their 298-6 at Leeds in 1990 as they raced past 300 for the first time since their inaugural meeting in 1973.
Vincent and Taylor shared a third wicket partnership of 137 after Plunkett dismissed Stephen Fleming and Peter Fulton (both for 15) while Oram smacked his unbeaten fifty off just 33 balls at the end of the innings.
Oram scored a hundred off 71 balls in his team's narrow loss to Australia on Sunday and continued his brilliant form with four sixes and three fours.
Taylor and Brendon McCullum (19) also cleared the ropes while Vincent and Taylor both struck seven boundaries as England's bowlers struggled to maintain their line, sending down 22 wides in the 50 overs.
England needed to win the match to have any real hope of making the finals against Australia but had to show a dramatic improvement with the bat to overhaul New Zealand's score after making just 120 and 110 in their last two matches.
New Zealand 318 for 7 in 50 overs (Lou Vincent 76, Ross Taylor 71, Jacob Oram 54 n o; Liam Plunkett 3 for 54, Panesar 2 for 35) Vs England (yet to bat)