(CNN) -- Bangladesh gave their Cricket World Cup quarterfinal hopes a boost with victory over the Netherlands while Pakistan sealed their progress with a rain-affected win against Zimbabwe.
Bangladesh, who are hosting the tournament along with South Asian neighbors India and Sri Lanka, have leapfrogged England into the final qualification spot in Group B after a comprehensive six-wicket win.
It means England need to beat the West Indies on Thursday to keep their hopes of making the last eight alive.
In Group A, Pakistan beat Zimbabwe by seven wickets to clinch their place in the knockout stages after Sri Lanka, New Zealand and Australia also booked their slots.
Bangladesh, buoyed by their victory over England on Friday, dismissed the Netherlands for just 160 in Chittagong.
Ryan ten Doeschate held their innings together with an unbeaten 53 but regular wickets meant the Dutch couldn't put any big partnerships together.
Abdur Razzak was the pick of Bangladesh's bowlers, taking three wickets for 29 runs in his ten overs. Netherlands' last five batsman added just seven runs to their total.
In reply, Imrul Kayes hit 73 not out to steer Bangladesh towards their target while Junaid Siddique added 35 and Shahriar Nafees made 37. Netherlands have lost all five of their matches at the tournament.
Bangladesh play their final game in the group stages against South Africa on Saturday but if West Indies beat England they will be through.
After the match Bangladesh captain Shakib Al Hasan told reporters: "It was a nervous game because we had to win to stay in the contest.
"We'll watch the West Indies v England game very closely, but we want to do well against South Africa."
Pakistan secured their progress to the last eight after Zimbabwe made 151-7 off 39.4 overs during a rain interrupted match in Kandy, Sri Lanka.
Craig Ervine top scored with 52 while fast bowler Umar Gul finished with figures of 3-36 off 7.4 overs.
Pakistan's adjusted target was 164, which they reached for the loss of just three wickets in 34.1 overs.
Mohammad Hafeez got their innings off to a fast start with a knock of 49 while Asad Shafiq hit 78 off 97 balls to ensure Pakistan's victory.