Capriati overcame a first-set loss to win, 4-6, 7-6 (7-5), 6-4, for her seventh triumph in as many career meetings against Shaughnessy.
On the men's side, No. 5 Carlos Moya of Spain battled back to edge upcoming American Robby Ginepri and advance to the final four at this event for the first time.
Capriati will meet the winner of a night match between No. 4 Justine Henin-Hardenne of Belgium and American Chanda Rubin. Henin-Hardenne and Rubin will meet for the fifth time, with the Belgian holding a 3-1 edge.
This is the fourth time Capriati has made the final four in 12 appearances. She was a runner-up the past two years to Venus and Serena Williams and also lost to Arantxa Sanchez-Vicario in the 1992 semis.
Shaughnessy, who upset Venus Williams in the fourth round, was in the quarterfinals for the first time in five visits here.
Moya pulled out a 6-7 (5-7), 6-3, 7-6 (7-4) triumph over Ginepri.
"It was a tough match. I think I made it more complicated," Moya said. "I had chances to win that first tiebreak, but he's a great player. I wasn't able to break his serve much."
Moya made his second semifinal of 2003, having captured the Buenos Aires claycourt event in February.
The 26-year-old is looking to win his second Tennis Masters Series event in as many years. He lifted the trophy in Cincinnati after overcoming world No. 1 Lleyton Hewitt in the title match.
The 20-year-old Ginepri became the first wild card entry to reach the quarterfinals here since Andy Roddick in 2001. The Fort Lauderdale native continued his strong play after making the last eight at Indian Wells earlier this month.
Moya awaits the winner of the Wednesday night's quarterfinal between No. 13 Paradorn Srichaphan of Thailand and unseeded Todd Martin of the United States.
Srichaphan, who last year was ATP's Most Improved Player, had a walkover in the previous round when Marcelo Rios withdrew with lower back pain.
Martin will be contesting his first quarterfinal in eight appearances here.