Garin pounded 27 forehand winners and fought off a second set comeback attempt to dispatch the struggling Norwegian, who has yet to win consecutive matches this season.
"I'm so happy with the way that I played," said Garin.
"I played so aggressive the whole match, even in the second set when I was leading 3-1 and lost those games I kept playing aggressive."
With the win Garin, a former top 20 player now ranked 97th, improved to 3-1 in his career record against Ruud.
"Casper is one of the players I really, really like on the tour so it's very special to me," said the Chilean.
Ruud is still searching for the sensational form that saw him make the finals of the French Open and US Open and soar up the rankings last year.
Garin will next face Russian Karen Khachanov (26) or Spaniard Alejandro Davidovich Fokina (23), who play later on Sunday.
On the women's side, seventh-seeded Maria Sakkari (27) of Greece kept her title hopes alive by battling back to beat Ukrainian Anhelina Kalinina (26) 3-6 6-2 6-4.
Sakkari drew Kalinina to the net with a drop shot and then fired a backhand winner down the line on match point to complete the comeback.
The Greek leaned over and pumped her fists in celebration after sealing the win on a hot day in the Southern California desert.
Sakkari, who made the final last year, will next face Czech 17th seed Karolina Pliskova (30) in the round of 16.
