In a low scoring encounter at the Brabourne Stadium England looked to have put themselves in pole position when they skittled out their opponents for just 147, Anya Shrubsole doing much of the damage with three for 24.
England's reply was woeful to start with as they crumbled to 39 for six, but a battling 49 from Lydia Greenway helped get them back on track.
More cheap wickets derailed the run chase again, however, leaving tail-enders Holly Colvin and Shrubsole as the last players standing with 34 runs still needed and plenty of overs remaining.
They chipped away at the total patiently and carefully to bring the runs required to just three, and in doing so set a new England record for a last-wicket stand in one-day internationals.
But the brave effort ended as Colvin was caught behind while attempting a cut leaving England all out for 145.
"We're disappointed to get so close," said skipper Charlotte Edwards.
"It was an important toss and I think we exploited the conditions well, and Anya bowled brilliantly up front.
"The reason we've lost this game is because of poor shots and a couple of bad decisions which have really cost us.
"We've got strength in depth in our order and we still believed we could win towards the end, and Holly played fantastically well.
"We're disappointed now but with this competition you've got to forget about it and move on to the next game, and hopefully we can win the last two."
In the day's other matches, New Zealand crushed Sri Lanka in their match in Mumbai, winning by eight wickets with an astonishing 162 balls remaining.
Sri Lanka batted first and were bowled out for 103 in 42 overs.
And New Zealand needed just 23 overs to complete a successful run chase, with Frances McKay's 39 not out leading the way.
West Indies also enjoyed a comfortable win as they overhauled South Africa's total of 230 with 27 balls remaining in Cuttack.
- Sports & Recreation
- Holly Colvin
- Anya Shrubsole
- Lydia Greenway