The Spaniard came into the day with a three shot lead but he had been replaced at the summit by the time he began his second round at 12.15pm, after early starter Wallace carded six birdies and a single bogey to set the clubhouse target at 12 under par.
And Otaegui looked in danger of falling off the pace completely in the early stages of his round, sandwiching the only birdie of his front nine - at the 15th - between bogeys on the 11th and 17th and fighting hard for pars elsewhere.
But his back nine was a different story, as he made four birdies and just the one bogey to head into the weekend tied for the lead.
Englishman Wallace, meanwhile, continued his impressive recent form, making the most of favourable morning scoring conditions to shoot a 67.
Aberdeen Standard Investments Scottish Open champion Aaron Rai sat a single shot behind the co-leaders after producing a brilliant 67 that contained two eagles in his first six holes, with France's Adrien Saddier another stroke back on ten under.
While others were racking up the birdies in pleasant conditions at Fairmont St Andrews, Otaegui struggled to replicate Thursday's form in the first few holes of his second round, slipping back to nine under with a bogey at the 11th.
He bounced back with a birdie from four feet on the 15th and could have made another at the next but his long putt ran five feet past the hole and he did well to save par.
Otaegui dropped another shot at the 17th before holing his 20 foot effort on the first green to return to ten under.
A third bogey followed at the second as the two time European Tour winner struggled for consistency but he rolled in for a birdie from eight feet on the fourth green before reeling off back to back gains courtesy of close range putts at the sixth and seventh to move alongside Wallace at the top.
Both of Otaegui's victories have come in match play events and he has his sights fixed on winning a stroke play tournament soon.
He said: "I'm feeling good, I'm feeling happy about the round. I had to work hard at the beginning to save some pars, which I did OK.
"And then I played much better on the back nine so it's been OK, it's been a good day.
"I'm pleased because of the way I've been playing in the last two days, the way I've felt on the greens as well, even if today I didn't hole as many putts as yesterday.
"Even when I struggled, the few shots I missed, I still fought to save par or try to save. There's still a lot of golf to play from now to the end of the week so let's go and enjoy.
"My favourite way of golf is stroke play so I definitely want to win that way as well."
Wallace had begun the day three shots adrift of overnight leader Otaegui but set about closing the gap with a birdie at the long 12th - his third hole.
The four time European Tour champion dropped a shot at the next but fired a bounce back birdie on the 14th to return to eight under.
Wallace holed his ten foot birdie putt at the 18th before making it back to back gains at the first.
After a run of four straight pars, Wallace reeled off back to back birdies at the sixth and seventh to get to 12 under.
The World Number 51 almost made it three in a row but his lengthy birdie putt on the eighth green narrowly missed the hole.
The Englishman gave himself another chance at the last, sending his approach into the ninth to 20 feet, but left his putt just short.
Wallace spent his first two rounds in the company of Padraig Harrington but he does not think his performances will influence the Ryder Cup Captain's thinking ahead of next year's rescheduled contest at Whistling Straits.
"It's good that I've done that in front of him but I'm not sure it'll make much difference to Padraig," said Wallace, who is looking to make his debut in the contest.
"He'll want players to be in there on merit and then if it comes down to a pick then he'll want to choose someone that's in form.
"I'm going to try and do it where I don't need to get a pick this time. This is a nice start. I'm taking in some form over the last few weeks, just not really posting any numbers.
"Hopefully I can do that this week."