Chawrasia, who has been dividing his time between Asian and European Tours, had three birdies in each of the first two rounds, but his rounds of 75 and 71 were not enough to keep him around for the weekend.
McIlroy, who is the tournament host, also exited with 72 and 73 in the two rounds.
Also failing to make the cut was Westwood (76-73) and Nicolas Colsaerts (72-77). The cut fell at a very good score of three-under. The 2016 Masters Champion, Danny Willett withdrew after a first round 71.
World Number 11 Jon Rahm also carded a 67 to sit a shot back, one ahead of New Zealander Ryan Fox who signed for a 66 in the third of the Rolex Series events with a prize fund of USD 7 million.
Hideki Matsuyama was in the clubhouse at nine-under alongside fellow Japanese Hideto Tanihara, with England's Anthony Wall also at that mark after seven holes of his second round.