The Scot, who had started the day six shots off the pace in Kuala Lumpur, jumped 23 spots to joint-third after firing a nine-under-par 63.
Knox, who defends his WGC-HSBC Champions title in Shanghai next week, carded nine birdies in a flawless effort as he moved within three shots of defending champion Justin Thomas (64-66).
In the second event of the new PGA Tour season, having skipped last week’s Safeway Open in California, Knox had already picked up shots at the first, third and fifth, 10th and 11th before reeling off four birdies in a row from the 14th.
The last of those was set up by an approach to six feet at the 336-yard 17th hole.
Knox finished 21st in the same event 12 months ago before landing his WGC win - he was the first Scot to claim one of those titles - the following week.
On-form Scot Marc Warren shot an eight under par 63 to top the leaderboard following the opening day of the Portugal Masters in Vilamoura.
The 35-year-old began with six successive birdies at Victoria Clube de Golfe before adding a further three after blemishing his card slightly with a bogey on the seventh.
Warren had been fighting to hang on to his European Tour card before finishing fifth in the Alfred Dunhill Links Championship just under a fortnight ago before following that up with another solid performance in last week’s British Masters.
Having jumped from 125th to 68th in the Race to Dubai on the back of those efforts, he now has the season-ending DP World Tour Championship in his sights instead of facing the prospect of a return to the Qualifying School.
Fellow Scot Paul Lawrie also made a promising start in Vilamoura with a 66 while Stephen Gallacher maintained his recent return to form with a 67.
Fighting to stay inside the top 111 in the Race to Dubai and thereby retain their playing privileges for next season, 107th-ranked Scott Jamieson had a 69 but Craig Lee, sitting 110th, faces a battle to make the cut following a 73.
Perth man Daniel Young shot one of the best scores of the day to leap up the leaderboard in the second round of the Alps Tour’s Grand Final in Italy.
The Scot reeled off six birdies in a row en route to a six-under-par 65 at Miglianico Country Club to move into a share of 12th spot.
Young, who lost in the final of the Scottish Amateur at Muirfield last year, started birdie-bogey before that hot streak from the fourth took him out in 30.
He then dropped shots at the 11th and 12th before bouncing back with a couple of late birdies.
Spaniard David Morago leads on 10-under after rounds of 65 and 67.
Dunbar’s Neil Fenwick and Ryan Campbell (Falkirk) are the leading Scots after two rounds in the PGA EuroPro Tour’s Tour Championship at Desert Springs in Spain.
Fenwick posted a second-round 69 while Campell carded a 70 as both players reached the halfway stage on five-under to sit seven shots off the lead in joint-14th.
Englishman Joe Dean stormed three shots clear at the top of the leaderboard in the £90,000 event as he backed up an opening 67 with a superb 65.
Compatriot Ashley Chesters, a member of last year’s winning Walker Cup side, is the Yorkshireman’s closest challenger.
Former Scotland international Brian Soutar (Leven Golf Society) made it two wins in a row in the Midland Golfers’ Alliance as a five-under-par 65 at Downfield left him five shots clear of the field at the Dundee venue.