Bhullar carded a flawless six-under 66 and moved up through the field from overnight tied 13th to tied third in the company of five-time Major winner, Phil Mickelson (63) with a score of 10-under 202.
However, Bhullar and Mickelson gained a place to tied second, following the two shots penalty handed out to Rory McIlroy (70) for an incorrect drop, which pushed the former World No. 1 to the fourth spot at nine-under 207.
Bhullar and Mickelson will likely play together with the leader Lee in lead group on the final day.
The European Tour Chief Referee John Paramor explained, "Rory's ball came to rest in a marked gallery crosswalk to the left of the second fairway from which relief is available under the rules, as if it's a piece of ground under repair.
More From This Section
"He found what he thought to be his nearest point of relief where the ball was outside and when he dropped the ball within a club's length, when he actually stood to the ball, his left foot was standing on or just over the line demarking the area of ground under repair which is treated as part of the ground under repair.
Bhullar had six birdies, four of them on front nine on first, second, sixth and eighth. Then he added two more on 11th and 15th.
Mickelson had a stunning nine-under 63 which also included two bogeys and an eagle. He had nine other birdes, four on front nine and five on the second half.
Leader Lee had five birdies and two bogeys.
After finishing his third round, Bhullar said: "I saw a lot of familiar faces on the back nine. There were quite a few Indian supporters walking and following me. It kind of really motivates me and hope to see these guys coming out in a big number tomorrow.