Robson, who made it to the semi-finals of WTA Palermo last week, fell at the first hurdle in Bastad as she lost 6-4 7-6(4) to Spanish third seed Anabel Medina Garrigues.
The British world number 91 went toe-to-toe throughout against a veteran ranked 56 places above her, with both players earning plenty of break point chances.
The match ultimately came down to a few key points which Garrigues showed all her experience to win.
The first set was close but Keothavong was then bageled in the second as she suffered a 6-4 6-0 defeat.
There was better news for British tennis when Heather Watson later beat Eleni Daniilidou of Greece 6-3 6-3 to reach the second round of the tournament held near San Diego.
Fifth seed Christina McHale delighted the home crowd with a 7-6(5) 7-5 victory over Jarmila Gajdosova of Australia while McHale's fellow American Vania King also won through, with a routine 6-1 6-4 success over Chang Kai-Chen of Taiwan.
But Coco Vandeweghe, a finalist in Stanford last week, fell to number eight seed Chanelle Scheepers, the South African prevailing 6-2 7-6(4).
Completing the day's action were Melinda Czink, who beat Sesil Karatantcheva 6-2 4-6 7-5, and Melanie Oudin, a 1-6 7-6(6) 6-0 winner against fellow American Sloane Stephens.
Back in Sweden, second seed Julia Goerges and sixth seed Klara Zakopalova came safely through their opening matches.
Germany's Goerges won 6-2 6-2 against Czech Barbora Zahlavova Strycova, who was runner-up in Palermo at the weekend, while Strycova's fellow Czech Zakopalova beat Annika Beck of Germany 2-6 6-3 6-4.
Two local wildcards went out at the first stage, with Dutch player Arantxa Rus beating Rebecca Peterson 6-1 6-2 and Colombian qualifier Mariana Duque beating Sandra Roma 7-5 6-1.
Spain's Silvia Soler Espinosa beat Georgia's Anna Tatishvili 4-6 6-3 6-0, while Ukraine's Kateryna Bondarenko beat Germany's Carina Witthoeft 6-2 7-6(5).