The setback ended Agassi's run at a potential ninth Grand Slam title.
Agassi, 33, who won his third straight Australian Open in January, won three of his first four matches at Roland Garros in straight sets, and rallied from two down to survive the other.
He would have regained the No. 1 world ranking if he reached the final, taking over for Lleyton Hewitt, who already was out.
Coria, 21, a former junior champion at Roland Garros, lost both of his prior meetings with Agassi, whom he referred to as his "hero," but both of those meetings were on hard courts.
"I'm very happy because I'm never going to forget this throughout my life," said the seventh-seeded Coria, a former junior champion at Roland Garros, who has won 19 of his last 21 matches.
Agassi appreciated the compliment, but still was disappointed with the setback. He was seeking his second straight Grand title, having won his third consecutive Australian Open title in January.
"I'd rather not be his idol and play him on hard court than be his idol and play him on clay," Agassi said.
Coria is the fourth different Argentine to reach the French semifinals in the Open Era. With his quick feet and a variety of shots, the Hamburg champion has won 19 of his last 22 matches.
"If you had told me one year ago that I was going to play Carlos Moya in the Roland Garros quarterfinals and beat him, I would have thought that we ought to drink more beer and then I might believe you," Verkerk said.
On the women's end, top-seeded Serena Williams, the defending champion, breezed into the semifinals with a 6-1, 6-2 victory over crowd favorite Amelie Mauresmo.
"It's difficult when you play a player who the crowd loves so much and who does so much for the country and you're playing her in their country," Williams said.
Williams is aiming for her fifth straight Grand Slam title. While it's three tournaments away, she also is looking to become the first player since Steffi Graf in 1988 to win all four majors in the same year.
Williams' semifinal opponent will be fourth-seeded Justin Henin-Hardenne of Belgium, who handed the world's top-ranked player her first loss of the season in early April at the Family Circle Cup final.
Henin-Hardenne bounced No. 8 Chanda Rubin, 6-3, 6-2, as she seeks her first career Grand Slam title. She reached the semifinals for the fifth time.
The other semifinal will pit second-seeded Kim Clijsters of Belgium and unseeded Nadia Petrova of Russia.
Clijsters crushed No. 24 Conchita Martinez of Spain, 6-2, 6-1, and Petrova outlasted fellow Russian Vera Zvonareva, the 22nd seed, 6-1, 4-6, 6-3.