Randhawa, who has been playing a limited schedule, made up just enough on the back nine with three birdies and squeezed inside the cutline.
Randhawa had rounds of 70 (at Kingsbarns), 69 (at Old Course, St Andrews) and 71 at Carnoustie to total six-under 210 and be in tied-50th place after 54 holes.
However, the other three Indians -- Shiv Kapur (75 at Old Course, 70 at Kingsbarns and 70 at Carnoustie) at one-under 215; Jeev Milkha Singh (77 at St Andrews, 76 at Carnoustie and 73 at Kingsbarns) at 10-over and SSP Chawrasia (77 at Kingsbarns, 75 at Old Course, 75 at Carnoustie) at 11-over -- missed the cut.
The two-time European Tour winner took advantage of ideal conditions at St Andrews, firing eight birdies and a solitary bogey to move to 17 under par.
Germany's Florian Fritsch is three strokes further back on 14 under after notching six birdies and an eagle at Kingsbarns.
Frenchman Benjamin Hebert finished day three on 13 under after mixing six birdies with a single bogey at Carnoustie. Kiradech Aphibarnrat is among the group at tied-4th on 12 under after carding eight birdies and two bogeys at St Andrews, alongside young Swede Joakim Lagergren, who fired an eagle and eight birdies in a flawless 62 at Kingsbarns.
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