With a place in the finals up for grabs in the last qualifying match, England looked in trouble at 52 for three after captain Michael Vaughan had won the toss and elected to bat on Tuesday.
However, Collingwood (106) and Strauss (55) steadied the innings with a 123-run fourth-wicket stand, both players making their first substantial scores of the series.
Collingwood had been horribly out of touch, but returned after missing last Friday's win over Australia due to illness to score a superb and much-needed hundred.
He made the most of an early life, with Black Caps allrounder Jacob Oram grassing a caught-and-bowled opportunity when Collingwood was 18.
Collingwood, who also teamed with James Dalrymple for a handy partnership of 59 in the latter overs, brought up his third one-day international century when he pushed Shane Bond down to long-on for two.
He was eventually bowled around his legs by Bond in the 48th over as he looked for quick runs, having faced 121 balls and hit eight fours.
Strauss had made a lot of starts without capitalising and reached 50 for just the second time since arriving in Australia in early November.
He finally had some luck with the umpires, surviving a confident lbw appeal before eventually being bowled by Scott Styris.
The Kiwis were considering resting the injury-plagued Bond for the match, but their decision to risk him with a finals berth on the line paid off when Bond claimed two early scalps and finished with 4-46 to be clearly his side's most effective bowler.
Bond should have had five wickets, with Peter Fulton dropping a simple catch as England took 16 off the final over of the innings.
Vaughan's testing series continued when he fell for a duck.
Having missed the last five games of his comeback series after knee surgery with a hamstring strain, Vaughan watched as Bond's first delivery sailed through innocuously for a wide.
The next delivery was a perfect inswinging yorker that crashed through his defences and hit middle stump.
In a superb opening spell, Bond then found the edge of Ian Bell's bat and the right-hander was neatly caught by Styris in slip for 12.
Fellow opener Ed Joyce was again hitting the ball well, but backed away and tried one big shot too many, edging James Franklin through to wicketkeeper Brendon McCullum on 28 to leave the English teetering at 52-3.
England 270 for 7 in 50 overs (P Collingwood 106, Andrew Strauss 55, Dalrymple 29, Ed Joyce 26; Shane Bond 4 for 46, James Franklin 1 for 45) Vs New Zealand (yet to bat)