TPC Southwind gave nothing away easily on Saturday, with a swirling wind and tough pin positions ensuring that the field remained congested heading into the Sunday's running, with one shot separating the top four.
Overnight leader Brooks Kopeka moved to 10-under at one point, only to falter in a round of 71 that sees him in a share of second with Scott Brown.
Owen, who has made just seven of 12 cuts in 2015, and Gomez are both bidding to become first-time winners on the PGA Tour, and they were two of six players who held the lead at some point during the third round.
Gomez began the day with a bogey at the first, but bounced back with four birdies in five holes from the second to the sixth to move to nine-under and a share of the lead. However, a bogey at the 11th after finding the sand and a further dropped shot at the 13th saw him fall back, but back-to-back birdies at the 15th and 16th saw the Argentinean once again hit the front.
Birdies at the third at seventh holes saw Owen take the turn in 33. A bogey at the 10th was followed by a birdie at the par-three 14th hole which saw him join Gomez at the front of the pack. A further birdie at the 18th after hitting his approach within five feet ensured the Englishman would stay there.
Koepka quickly erased any thoughts of a bogey at the second with a fine eagle at the third after sinking a 20-foot putt for a three at the par-five. However, a bogey at the fourth after finding water from the tee was followed by another dropped shot at the fifth as Koepka fell to eight-under where he remained for the day.
After beginning the third round in second, Austin Cook briefly enjoyed a three-way share of the lead with Owen and Gomez, but the American was two-over for the back nine and had to settle for a tie for fifth on six-under where he is joined by Australian Matt Jones.
A group of eight players which includes Ryan Palmer, Chris Smith, David Toms and Chad Campbell are on five-under, with Phil Mickelson a further two shots back.
Former world number one Luke Donald (72) and defending champion Ben Crane (74) saw their hopes of victory all but ended as they find themselves on one-under and even-par respectively.