Safarova was appearing on the WTA Tour for the first time since reaching the Wimbledon semi-finals, but the Czech left-hander was dumped out of the WTA International event by France's Kristina Mladenovic.
Mladenovic was a first-round loser at SW19, but had won five matches on hard courts at WTA level since - and it looked her recent experience on the surface was the difference in Washington.
The 78th-ranked Mladenovic posted a 2-6 6-3 6-3 triumph in two hours five minutes.
Rybarikova's quest for a three-peat in the American capital was swiftly ended by Russian second seed Ekaterina Makarova, who sauntered to a 6-1 6-1 victory in 52 minutes.
Fourth seed Sloane Stephens' struggles continued, as she lost to fellow American Christina McHale 6-4 4-6 6-0.
Russia's fifth seed Anastasia Pavlyuchenkova was a 6-2 6-2 winner over Frenchwoman Virginie Razzano.
Serbia's Bojana Jovanovski endured an almighty challenge from Australian qualifier Olivia Rogowska before advancing 6-7 (5-7) 7-5 7-5 in two hours 35 minutes.
New Zealand's Marina Erakovic broke a four-match losing streak on tour, with a 4-6 6-2 6-4 triumph over Czech Kristyna Pliskova.
American Lauren Davis came from behind to down China's Peng Shuai 1-6 6-4 6-2, and Belgium's Kirsten Flipkens edged Briton Heather Watson 6-3 1-6 7-6 (7-3).