Eoin Morgan starred with 40 after England, chasing 150 for victory, had slumped to 66 for four at the Beausejour Stadium.
But, together with Luke Wright, who made 24, the former Ireland left-hander swung the game back England´s way in a stand of 52 in just more than six overs.
Morgan got out just before the finish but man-of-the-match Tim Bresnan, unbeaten on 23 after taking one wicket for 20, ended the contest with five balls to spare when he pulled Kyle Mills for four.
England, already through to the semi-finals before this final Group E match even started, after defending champions Pakistan beat South Africa earlier in the day, ended the Super Eights with a perfect played three won three record.
They will now face the runners-up in Group F in the first semi-final here on Thursday.
"It´s crucial that you keep the momentum going and stay in winning ways," said England captain Paul Collingwood at the post-match presentation ceremony.
"There´s areas to improve on again, but I´m absolutely delighted in how we´ve gone. A lot of credit goes to the bowlers."
England´s victory also meant Pakistan went through to the semi-finals as group runners-up after edging New Zealand on superior run-rate.
New Zealand captain Daniel Vettori blamed repeated batting failures for his side´s exit.
"There were a number of factors (in losing this match), 150 was competitive but about 10 below par," Vettori said.
"We did well to fight back but Morgan and Wright´s partnership took it away from us. We could have bowled better. We just haven´t been able to put enough runs on the board."
Meanwhile Bresnan was delighted by his all-round display.
"I´ve definitely got two strings to my bow and I do like batting at the end when I can play my shots. As long as you bowl the ball in the right spot, it´s hard for the batsman."
England had won their previous matches against Pakistan and Sri Lanka on the back of Pietersen fifties.
But they had to do without their star batsman after Pietersen, who expects to be back for the semi-finals, was given temporary leave to attend the birth of his first child, a boy, which took place in London on Monday.
England made a rousing start to their run chase with Craig Kieswetter, like Pietersen and Michael Lumb born in South Africa, launching Nathan McCullum´s off-spin for a four and a huge six in successive balls as 13 runs came off the first over.
But England then lost Kieswetter when the wicketkeeper struck Kyle Mills hard but straight to Nathan McCullum at cover-point.
Lumb on drove the express pace of Shane Bond for a huge six and twice swept left-arm spinner Vettori for four.
Ravi Bopara, Pietersen´s stand-in, made just nine before he was well caught in the covers by Ross Taylor off all-rounder Scott Styris for nine.
The 60 for two became 60 for three when Lumb was plumb lbw for 32, made off 21 balls with a six and four fours, after he missed a sweep against Vettori.
England´s collapse continued to 66 for four when Collingwood was deceived by a Styris slower ball and clipped straight to Brendon McCullum at midwicket.
However, Morgan struck an amazing one-handed six off Styris and Wright crashed a couple of boundaries off fast bowler Ian Butler.
Morgan´s 34-ball innings ended when he pulled Bond and Vettori took a fine diving catch but it was too little too late for New Zealand.
Earlier Ross Taylor top-scored for New Zealand with 44 and put on 62 for the fourth wicket with Styris (31) after the Black Caps slumped to 65 for three.
Pakistan beat South Africa by 11 runs
Defending champions Pakistan beat South Africa by 11 runs to knock the Proteas out of the World Twenty20 and keep their own semi-final hopes alive on Monday.
In a must-win game for both sides, Pakistan were in dire straits at 18 for three but made 148 for seven thanks mainly to man-of-the-match Umar Akmal´s 51.
South Africa, chasing a relatively modest target, were then held to 137 for seven with spin, primarily off-break bowler Saeed Ajmal (four wickets for 26 runs), proving their undoing.
The Proteas slumped to 68 for four and despite a fifty from AB de Villiers couldn´t break the Pakistan slow bowlers´ stranglehold.
Now Pakistan must hope England, already through to the semi-finals following this result, beat New Zealand by a sufficiently wide margin later here on Monday to allow the title-holders through to the last four on net run-rate.
Victory for New Zealand would secure their semi-final spot.
Pakistan had an early wicket when Herschelle Gibbs (three) was caught at mid-on by Misbah-ul-Haq off all-rounder Abdul Razzaq.
It looked as if the batsman was early on the shot, undone by the slower pace of a Beausejour pitch slower than the one South Africa had grown used to in Barbados.
South Africa were now 12 for one and that became 23 for two when captain Graeme Smith chipped spinner Abdur Rehman to rival skipper Shahid Afridi at mid-off.
Jacques Kallis was caught in the deep off Ajmal for 22 and Rehman struck again to get rid of JP Duminy after Umar Akmal, running in from long-on, took a fine catch.
De Villiers though was still there.
But his 53 off 41 balls came to an end when he tried to play an audacious scoop shot off Ajmal and skied a simple catch to wicketkeeper Kamran Akmal to leave the Proteas 101 for five.
South Africa, who needed 51 off the last five overs, then saw the experienced Mark Boucher lbw to Ajmal for 12.
They eventually got the target down to 17 off the last over, from Ajmal.
Four singles followed before Botha was stumped by wicketkeeper Kamran Akmal and that left South Africa needing an impossible 14 runs off two balls.
Earlier, a stand of 51 in six overs between Umar Akmal and brother Kamran (37) revived the innings before Umar put on 61 with Afridi (30), who´d won the toss.
Fast-medium bowler Charl Langeveldt, maintaining an admirable line, took a career-best four wickets for just 19 runs from his maximum four overs.
South Africa´s seamers had early success but the Akmal brothers got the innings going again, Kamran slog-sweeping Roelof van der Merwe and Umar playing a similar stroke for six against the left-arm spinner.
Umar Akmal reached his 31-ball fifty in style with a fourth six, driven straight off Langeveldt.
But, two balls later, he failed to clear the boundary and was caught by Gibbs off Langeveldt.
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