The 34-year-old from Las Palmas, who teed off on the 10th, nearly capped a superb performance with an ace at the par-three second, drilling his tee-shot to within a foot of the pin.
English player Fleetwood moved to nine under after hitting a 66. Starting on the tenth tee, Sloan made five birdies in six holes from the 12th to the 17th, keeping the momentum going with a delicate sand save on the 15th from a tough lie in the bunker.
Cabrera-Bello - a three-time European Tour victor but seeking his maiden PGA Tour crown - started his day with birdies on four of his first six holes to jump out to an early lead.
"There's a lot of challenging shots", Cabrera Bello said.
"Honestly, the way the greens are, they are so firm and they are getting so fast, the only way I feel like I can stop the ball on the greens is by playing high cuts". "I didn't want to play that shot again". "To win an event that has the name of one of the greatest players on earth would be really special, but it's only Thursday".
The defending champion got off to a sluggish start in Orlando, sandwiching a birdie at the 13th (his fourth) between bogeys at the 11th and 18th.
Mickelson's double-bogey came at the expense of one of the more daring shots of the day as the five-time major victor attempted a right-handed effort behind a net.
Mickelson then took a drop and eventually wracked up a double bogey but in typical lefty style still managed to shoot 68 and head to the second round T3.
The Northern Irishman's only blot in his round was a bogey at the par-four eighth but, after six successive pars, the four-time major champion finished with three further gains, including a closing birdie, and he was particularly pleased with one facet of his game.
Rory McIlroy is seven shots behind clubhouse leader Tommy Fleetwood after hitting a two-under-par 70 on day two at the Arnold Palmer Invitational.
Phil Mickelson, who was a late addition to the field, didn't make the cut after shooting a 6-over 78.
The prestigious US PGA Tour event at Bay Hill will field six of the world's top 10 golfers and 13 of the top 20, despite eight-time event victor Tiger Woods withdrawing on tournament eve.
Day told the PGA Tour that he had an MRI on Monday that revealed he has a tear in a disk in his lower back.