Pakistan hammered Bangladesh by 94 runs at Lord's but failed in their highly unlikely task of pipping New Zealand to the last World Cup semi-final place.
The 1992 winners needed victory by a record margin of at least 308 runs to finish fourth on a better net run-rate.
An Imam ul-Haq century and 96 from Babar Azam saw them post 315-9 before they dismissed Bangladesh for 221.
Shakib Al Hasan top-scored with 64 for the Tigers but seamer Shaheen Afridi (6-35) produced a match-winning spell.
Pakistan could not reach the semi-finals once Bangladesh reached 8-0 in the second over of their chase, confirming New Zealand in the last four with Australia, India and England.
England will finish third and New Zealand fourth, with the group winners to be decided on Saturday.
Leaders Australia will top the group if they beat South Africa at Old Trafford (13:30 BST) but if the defending champions lose, India can overtake them by defeating Sri Lanka at Headingley (10:30 BST).
| World Cup group table | ||||||||
|---|---|---|---|---|---|---|---|---|
| Rank | Team | P | W | L | T | NR | RR | Pts |
| 1 | Australia (Q) | 8 | 7 | 1 | 0 | 0 | 1 | 14 |
| 2 | India (Q) | 8 | 6 | 1 | 0 | 1 | 0.811 | 13 |
| 3 | England (Q) | 9 | 6 | 3 | 0 | 0 | 1.152 | 12 |
| 4 | New Zealand (Q) | 9 | 5 | 3 | 0 | 1 | 0.175 | 11 |
| 5 | Pakistan | 9 | 5 | 3 | 0 | 1 | -0.43 | 11 |
| 6 | Sri Lanka | 8 | 3 | 3 | 0 | 2 | -0.934 | 8 |
| 7 | Bangladesh | 9 | 3 | 5 | 0 | 1 | -0.41 | 7 |
| 8 | South Africa | 8 | 2 | 5 | 0 | 1 | -0.08 | 5 |
| 9 | West Indies | 9 | 2 | 6 | 0 | 1 | -0.225 | 5 |
| 10 | Afghanistan | 9 | 0 | 9 | 0 | 0 | -1.322 | 0 |
Realistically, Pakistan knew their tournament was all but over before a ball was bowled at headquarters, even though captain Sarfaraz Ahmed said: "If Allah helps then miracles can happen."
There remained the smallest of chances a record-breaking one-day international victory could see them sneak into the semi-finals on net run-rate.
The minimum score they needed to stand any theoretical chance was 308 but even that would have meant Bangladesh needing to be bowled out for nought.
In the end, they stuttered their way to 315-9 despite Imam and Babar providing the platform with their 157 partnership off 151 balls for the second wicket.
But when the latter was dismissed hit wicket a ball after recording his seventh ODI century, 246-2 in the 42nd over was perhaps not fully capitalised upon.
Imad Wasim (43) did launch a counter-attack with some lusty blows despite striking skipper Sarfaraz on the arm at one stage, forcing him to retire hurt.
Ultimately, neither that nor the injury would cost Pakistan with the wicketkeeper able to resume his innings off the last ball before adding a catch and a stumping in the field.
Shaheen's figures were both his first five-wicket haul in ODI cricket and the best figures by a Pakistan bowler in a World Cup match.
Bangladesh came to this World Cup as dangerous underdogs and caused a couple of upsets along the way.
But amid memorable victories against South Africa and West Indies have been disappointing defeats such as this, where stand-out individual performances have lacked support.
Here Mustafizur Rahman took 5-75 to become the second-highest wicket taker at the tournament on 20 behind Australia's Mitchell Starc with 24.
Then with the bat, Shakib reinstated himself at the top of the run-scoring charts on 606 with his seventh score of 50 or more in this competition, including two centuries, which equalled Sachin Tendulkar's record for India from 2003.
Their coach Steve Rhodes, the former Worcestershire and England wicketkeeper, will no doubt take the positives from their victories but will also be aware what might have been in some of their closer-fought defeats.
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