Wallace took advantage of the favorable morning conditions by making six birdies and a single bogey to get 12 under par.
He went into the clubhouse with a two-shot lead but Otaegui, the overnight front runner, struggled hard on his afternoon round and improved his fortune to his back nine. There the Spaniard made four birdies and a bogey to pursue his opening round of 62 with a 70.
Aaron Rai, the winner of the Scottish Open two weeks ago, made two eagles in his first six holes and was one shot back.
Highlights: Wallace, Otaegui co-lead weekend in Scotland
Full field results from the Scottish Championship
The French Adrien Saddier was fourth with 10 under, after a final bird on the 18th gave him a pair of 67s.
Ryder Cup captain Padraig Harrington carded a 69 to put him at 9 under a three-way tie for fifth.
Lee Westwood carded a 70 and was in a group of players five shots away from the lead.
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