Meanwhile, British wildcards Freya Christie and Eden Silva fell to a straight-set loss against Australian duo Kimberly Birrell and Talia Gibson in the first round of the women’s doubles.
In the mixed doubles, Glasspool and Czech Tereza Mihalikova defeated American-German wildcards Venus Williams and Kevin Krawietz 6-4 6-4 to reach the second round.
British pair Marcus Willis and Heather Watson are also into the second round after coming from a set down to beat Poland’s Jan Zielinski and Taiwan’s Hsieh Su-wei.
But fourth seeds Patten and fellow Briton Olivia Nicholls fell to a straight-set defeat by American Evan King and Canadian Gabriela Dabrowski.
Britons Luke Johnson and Emily Appleton also fell at the final hurdle against American-Kazakh pair James Tracy and Anna Danilina.