Branden Grace, a back-to-back winner on The European Tour already this year, highlighted the good scoring possible with a superb 64. The South African had an incredible eight birdies in his first 11 holes before paring his way in to climb from 71st overnight to 43rd.
McIlroy followed his early brace of birdies with a hat-trick from the fifth.
By holing from eight, three and ten feet the 22 year old US Open Champion had already charged from 28th to joint seventh and from ten behind Watson to only five back.
Tiger Woods, second to him at the Honda Classic last week, was only one behind him after he started with a two-putt birdie - and Lee Westwood made it four birdies in a row around the turn to improve to four under.
McIlroy had to settle for par on the long eighth, as he had at the first, but a 14 footer for his sixth birdie on the ninth meant he turned in just 30 strokes and was joint fifth on eight under.
So was Woods after he sank putts of 18 feet at the second and two feet on the next to make it three in a row.
Laird, meanwhile, finished with a 66 to set the early clubhouse target of six under.