Shubhankar, the only multiple winner on the European Tour this season, followed up his first round 69 with a second round 72.
Chawrasia had a 73 on first day and managed only 71 on the second to finish at one-under 143 and exited as the cut fell at 4-under 140.
Shubhankar, starting the second day at 3-under, opened the second round with a bogey but quickly made up on the next hole. Seven aprs followed that before he bogeyed the Par-5 ninth.
It was his second successive missed cut after his superb win at Maybank Malaysian Championships early this month.
Shubhankar flies to Mexico, where he makes his WGC debut, while Chawrasia will go back home where he defends his Hero Indian Open, which he has won in both 2016 and 2017.
The Spaniard made birdies on the 16th, 17th and 18th to sign for a 66 at Doha Golf Club and get to 11-under. He had a 67 in the first round.
He leads from Scot Stephen Gallacher (68-66), Frenchman Grgory Havret (65-69), England's Eddie Pepperell (65-69) and South African Erik van Rooyen (68-66).
Otaegui won his first European Tour title at last season's Saltire Energy Paul Lawrie Match Play and has made his last nine cuts. After a bogey free first round of 67, he had just one bogey in his second round 66.
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