While Chawrasia shot 73-72 and finished way down Kapur (70) and Jeev (75) withdrew after the first rounds. The US Open will be held at Erin Hills next month.
Chawrasia was just unable to get his putter going and dropped a lot of shots in the first round and was unable to make up in the second.
Chawrasia and Kapur are now headed to Sweden for Nordea Masters later this week.
The Wolverhampton native, whose Indian origin parents came from Kenya, has won two events on the European Challenge Tour this season. He shots 66-64 and led the list of 15 qualifiers from the sectional.
Li Haotong of China, meanwhile, will also make his US Open debut at Erin Hills after he matched Rai's 64 in Round 2 to place second with a 13-under total.
Frenchman Alexander Levy will return to the US Open after he finished in a share of third place at 12-under par alongside 2006 US Amateur champion Richie Ramsay.
Andrew "Beef" Johnston, who was a fan favorite in his US Open debut at Oakmont Country Club last year, delighted the crowds at Walton Heath, making a hole-in-one on the second hole of the New Course during his morning round, and then recording a pair of eagles during Round 2 to earn his spot with one stroke to spare at 10-under 134.
The others to qualify in regulation were South Africans Oliver Bekker, George Coetzee and Brandon Stone, Frenchman Joel Stalter, Englishman Eddie Pepperell and Welshman Bradley Dredge.
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