Rai posted the joint best round of the day with an eight-under 64 to jump into a share of the lead with a round that included five birdies and an albatross – holing out from 214 yards on the par-five second.
Kobori trended in the opposite direction in his second round, with a three-over 73 seeing him fall into a tie for 24th after holding a share of the round-one lead.
The 24-year-old didn’t have a poor round as such, with three birdies and a bogey, but a triple bogey on the par-five 18th saw him end the day with an unflattering card.
At seven-under, he remains in a competitive position for the tournament will look to make a move in the third round.
The tournament also shapes up as a last chance for players to earn their place in the DP World Tour Championship, in which the top 50 players on the season leaderboard make the field.
Going into this week’s event in Abu Dhabi – which was limited to the top 75 – Kobori was ranked at No 38 with Hillier at No 20.
The tournament has a prize fund of US$9 million ($16m), with the winner taking home US$1.53m ($2.72m).