Woods ended the round equal second with fellow American Brandt Snedeker (67) and Englishman Justin Rose (66), with Canadian surprise package Conners continuing to lead, the PGA Tour rookie posting a 68 for a nine-under 204 total.
Sixteen-time Grand Slam champion Nadal, while holidaying in the Bahamas, turned up at the Albany Golf Course to watch Woods in action.
Tiger Woods birdied on holes 3, 8, 10, 13, 14 but lost the advantage with bogeys on the par-five 9 and 15.
Woods, who has undergone multiple back surgeries in his long and illustrious career, is set for his latest comeback at this week's Hero World Challenge.
Tiger Woods has not played since February after a recurrence of back problems which forced him to miss the 2015-2016 season
Tiger Woods pleaded guilty in a Florida court on Friday to reckless driving, the state attorney said, after police found the golf champion asleep in his Mercedes-Benz beside the road last May.
Tiger Woods hasn't played since February, when he withdrew from the Dubai Desert Classic. He has played three times in two years thanks to a series of injuries and had a fourth back surgery in April.
A urine test revealed four other medications along with hydrocodone -- which is sold under the brand name Vicodin.
The 41-year-old Woods once held the world number one ranking for a record 683 weeks.
Police in Jupiter, Florida, released dash-cam footage of the arrest of Tiger Woods for driving under the influence two days earlier.
The former world No 1 golfer was arrested on a DUI charge on Monday but was later released.
The 14-time major champion blamed his arrest on a reaction to a mixture of prescription medication he has been taking, insisting in an apology to fans that alcohol was not involved in the incident.
Former world No 1 golfer Tiger Woods was arrested for driving under the influence of alcohol but was later released.
Tiger Woods's historic 1997 victory at Augusta National, when he was 21 years old, was a watershed for golf.
Tiger Woods last won a major title at the 2008 US Open and last won any title at the 2013 WGC event in Akron, Ohio as he tries to win three more career PGA titles to match the record 82 won by Sam Snead
Golf great Tiger Woods played the sport with United States president-elect Donald Trump at Palm Beach, Florida.
Tiger Woods, who ended a 16-month layoff after back surgery, struggled to a four-over par 76 to finish 15th at the elite 18-man event at Albany Golf Club in the Bahamas.
Former world number one Tiger Woods, a 14-time major champion, shot his best sub-par round since a 10-under 62 in the second round of the 2013 edition of the elite 18-player event that benefits his charity foundation.