Echavarria moved into contention for the first win of his career since turning professional six years ago after rattling in six birdies and an eagle at Rio Grande's Grand Reserve Golf Club.
Echavarria began his third round charge early, bagging an eagle on the par-five second before a run of four straight birdies that started at the fourth to reach the turn at six under for the day.
"It was a dream start," Echavarria said. "You never think you're going to shoot six under on the front nine the third round."
The 28-year-old will head into Sunday's final round on 17 under, two shots ahead of American second round leader Carson Young, who salvaged a one-under-par 71 with a birdie on the 18th.
Sam Stevens and Nate Lashley are tied for third place on 13 under, four shots off the lead.
Stevens climbed 14 places up the leaderboard on Saturday with a seven-under-par 65 while Lashley made a move with a five-under-par 67.
Akshay Bhatia and England's Harry Hall share fifth place on 12 under, five adrift of Echavarria.
