The 40-year-old Englishman on Friday had five birdies and one bogey on a windy day at the par-71 El Camaleon course.
Summerhays birdied his final hole in a six-under 65 and first-round leader Claxton carded a 68 to share the lead on eight-under 134.
"I played really well today," said Owen, winner of the European Tour's 2003 British Masters. "Tough conditions and drove it in most of the fairways and just kept plugging away and took some chances.
"It's been a bit of wandering around in the wilderness for a couple of years, so it's nice to see play is back and it's nice to see a few putts drop in."
Chris Stroud was a stroke back after a 66 for 135.
Australian Robert Allenby, Sweden's Richard S. Johnson and Kevin Stadler were tied on 136. Johnson carded a 66, Allenby a 67 and Stadler a 68.
Summerhays had seven birdies and a bogey.
"I drove the ball perfectly, pretty much," Summerhays said. "I hit it really solid into the wind. It's a tough driving golf course."
He sank a 35-footer for birdie on the par-four second hole. At the par-three third he hit to inches away for another birdie.
"It kind of just set me at ease there," Summerhays said. "I'm looking forward to learning and just seeing how my emotions react. And that's the only way to become a champion, so I'm excited for the weekend."
Claxton's round included four birdies and one bogey.
"The wind was a little gustier today, but I've just kind of had good control over my ball," he said.
"I certainly had a couple of good breaks here and there and putted the ball well. I'm just doing all the things you do when you're playing well."
Course designer Greg Norman missed the cut with rounds of 79 and 73.
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