Swiss Wawrinka had his serve broken seven times after dropping his serve just once in his previous two matches in Indian Wells, one of the biggest events on the ATP Tour calendar outside of the four Grand Slams.
"It was a match without a brain," said Wawrinka of the two hour, 25 minute marathon match that had a total of 13 service breaks.
"I had a tough time staying focused and being patient. I still tried to fight," Wawrinka said.
"Two times I came back. I had the chance in the third set to break him and finish it at 5-5 and I didn't."
"In general he deserved to win."
Wawrinka, who is ranked fourth in the world, blasted six aces but had five double faults and won just 43 percent of his second serves.
Goffin's victory snaps a 14-match losing streak for the Belgian against top 10 opponents. His last win over a top 10 player was against No. 9 Milos Raonic in 2014 at the Basel tournament.
He advances to the quarterfinals of the joint ATP and WTA Tour event where he will face Marin Cilic who defeated France's Richard Gasquet 7-5, 5-7, 6-2 in another three set thriller.
Taking the court later in the day is Rafael Nadal, world number one Novak Djokovic and Japanese star Kei Nishikori.
World number one Serena Williams plays her quarter-final match against defending champion Simona Halep in the evening session.
Third seed Agnieszka Radwanska faces Petra Kvitova in the other women's quarter-final.
Swiss seventh seed Belinda Bencic made an early exit on Monday in the third round.