The 36-year-old Agassi, making his 17th and final appearance at the Washington event, had no answer to Stoppini's strong serve and crisp groundstrokes, losing 6-4, 6-3 in 62 minutes.
Agassi received a first-round bye and was playing his first match of the tournament.
Tuesday’s results:
Second round: 1-James Blake (US) beat Kevin Kim (US) 7-5, 3-6, 6-2; 11-Arnaud Clement (France) beat Ryan Sweeting (US) 6-2, 6-1; Marat Safin (Russia) beat 15-Nicolas Mahut (France) 6-3, 5-7, 6-4; Andrea Stoppini (Italy) beat 4-Andre Agassi (US) 6-4, 6-3; Wesley Moodie (South Africa) beat 6-Sebastien Grosjean (France) 6-4, 3-6, 6-3; 14-Tim Henman (Britain) beat Phillip King (US) 6-7 (3-7), 6-3, 7-5; Kenneth Carlsen (Denmark) beat 9-Paradorn Srichaphan (Thailand) 4-6, 7-6 (8-6), 6-3.
First round: Hyung-Taik Lee (South Korea) beat Frank Dancevic (Canada) 2-6, 6-3, 6-2; Gilles Muller (Luxembourg) beat Paul Capdeville (Chile) 3-6, 7-6 (9-7), 4-0 – Capdeville retired; Tomas Zib (Czech Republic) beat Jean-Rene Lisnard (Monaco) 7-5, 6-4; Edgardo Massa (Argentina) beat Somdev Dev Varman (India) 6-4, 6-0; Ramon Delgado (Paraguay) beat Peter Luczak (Australia) 6-4, 6-4; Teimuraz Gabashvili (Russia) beat Jean-Christophe Faurel (France) 6-3, 6-3; Vince Spadea (US) beat Roko Karanusic (Croatia) 7-5, 1-0 – Karanusic retired.
SHARAPOVA, HINGIS WIN
SAN DIEGO: Second seed Maria Sharapova overcame a slow start against fellow Russian Vasilisa Bardina before reeling off 10 of the last 11 games to record a 6-4, 6-1 second-round victory at the Acura Classic on Tuesday.
Earlier, eighth seed Martina Hingis marched into the third round with a 6-2, 6-3 win over American Meilen Tu.
Other seeded winners included number seven Nicole Vaidisova of the Czech Republic, who destroyed Spain's Virginia Ruano-Pascaul 6-1, 6-0.
Number 11 Daniela Hantuchova of Slovakia advanced when Czech Kveta Peschke retired from their first round match with a thigh injury when trailing 6-1, 4-0.
Results:
Second round: 7-Nicole Vaidisova (Czech Republic) beat Virginia Ruano (Spain) 6-1, 6-0; 2-Maria Sharapova (Russia) beat Vasilisa Bardina (Russia) 6-4, 6-1; 8-Martina Hingis (Switzerland) beat Meilen Tu (US) 6-2, 6-3.
First round: Sania Mirza (India) beat Meghann Shaughnessy (US) 6-3, 6-1; 11-Daniela Hantuchova (Slovakia) beat Kveta Peschke (Czech Republic) 6-1, 4-0 – Peschke retired; Elena Vesnina (Russia) beat 10-Anna-Lena Groenefeld (Germany) 3-6, 6-3, 6-3; Ashley Harkleroad (US) beat Jill Craybas (US) 6-2, 6-3; Anna Chakvetadze (Russia) beat Jelena Kostanic (Croatia) 6-4, 6-3; Vera Zvonareva (Russia) beat 13-Ai Sugiyama (Japan) 6-1, 7-5; Gisela Dulko (Argentina) beat Shahar Peer (Israel) 2-6, 6-3, 6-3; Alona Bondarenko (Ukraine) beat Ivana Lisjak (Croatia) 6-2, 7-6 (7-2); 15-Katarina Srebotnik (Slovenia) beat Marion Bartoli (France) 6-3, 6-0; Amy Frazier (US) beat Tatiana Golovin (France) 6-3, 7-6 (9-7).—Reuters