Those three are joined atop the leaderboard by Sweden's Peter Gustafsson and Peter Hanson, Scotsman Steven O'Hara and Emanuele Canonica from Italy.
Philip Walton, a three-time winner on the European Tour, leads a group of six players one stroke back at 1-under-par 71. He is joined there by Hennie Otto, Peter Lawrie, Miguel Angel Martin, Oskar Bergman and Marco Bernardini.
Borrego, a two-time winner on the European Tour, opened with a birdie on the par-5 10th on the Old Course at San Roque Club. He stumbled back to even par with a bogey at the 16th, but made the turn at minus-one thanks to a birdie at the 18th.
The 33-year-old tripped to another bogey at the par-4 first. Borrego got back into red figures with a birdie at the fifth and closed his round with a birdie at the par-5 ninth to join the leaders at 2 under.
Luna also began on the back nine and moved to minus-2 with birdies at the 11th and 15th. Around the turn, the 42-year-old bogeyed the first, but bounced back with a birdie at the par-3 third. Luna faltered to another bogey at the eighth, but closed with a birdie on No. 9.
'It was a good round,' said Luna. 'I tried to be in the right place all the time and I am putting well. The chances I had I made it. That's the key to shooting a good score. The condition of the golf course is excellent and it is a good test for us.'
Rivero started out by bogeying the par-4 first. The 49-year-old bounced back with birdies at three and four. After five straight pars, he joined the leaders at minus-2 with a birdie at the 10th. He closed with eight consecutive pars.
'This week I am just playing to enjoy myself and have fun with the other golfers,' Rivero said. 'I have no further aspirations and have no intention of coming back on tour. I want to play the Seniors Tour. That is my goal.'
Gustafsson picked up two birdies and one bogey on the front nine. On the back side, he carded three birdies over a four-hole stretch from the 13th to jump out in front at 4 under. However, he slid backwards with bogeys at each of the last two holes.
Hanson birdied his first two holes before parring the next seven on the back side. He stumbled to a bogey on the first, but came right back with a birdie on the second. The 27-year-old bogeyed the eighth before a birdie at the ninth gave him a share of the lead.
O'Hara tripped to a bogey on the par-4 sixth. He got that stroke back with a birdie at the par-5 ninth and picked up consecutive birdies from the 13th to get to 2 under before parring his final four holes.
Canonica played the first nine holes with one birdie and one bogey. He dropped another stroke on the 12th, but got to even par with a birdie at 13. He then holed out for eagle on the par-4 15th to finish at minus-2.
Christian Cevaer, the defending champion, opened with a 5-over-par 77.