Mathieu, seeded sixth, fell 7-6 (7-2), 7-6 (7-3) to Pablo Cuevas while the seventh-seeded Istomin was beaten by Franco Skugor 7-6 (7-5), 7-6 (9-7) in the tournament's first round.
Fifth-seeded Tommy Robredo advanced to the second round, dumping Michal Przysiezny 7-6 (7-3), 6-3. Robredo didn't face a break point and lost 10 points in his 11 service games.
Jarkko Nieminen came away a winner of the only match on Tuesday's schedule that went three sets, beating Christian Lindell 4-6, 6-0, 6-4. Nieminen lost only eight points in the second set.
Also Tuesday, Andreas Seppi topped Marcel Granollers 6-4, 6-2; Ervin Eleskovic defeated Jerzy Janowicz; Andrey Golubev stopped Maximo Gonzalez 6-3, 6-2; and Stephane Robert beat Jonathan Dasnieres de Veigy 6-4, 6-1.