The trio - all ranked inside the top 25 on the WTA Tour - did not manage a set between them, with 12th seed Pennetta beaten by Kazakh qualifier Yulia Putintseva 7-6 (7-5) 6-3.
Pennetta, the world number 14, and Putintseva exchanged eight breaks of serve in the first 10 games, and both players coughed up several set points before it headed to a tie-break.
Contrary to the first set, both players found their serving range in the second - with one break in the fourth game the difference as the 164th-ranked Putintseva completed a big upset.
Errani, the 13th seed, was making her first tour hard-court appearance since March, and her rust on the surface showed as she lost to Germany's Sabine Lisicki 6-1 7-5.
Czech Barbora Zahlavova Strycova made it two wins from as many meetings with Vinci in 2014, trumping the Italian 7-5 7-5.
Next up for Zahlavova Strycova at the WTA Premier event is third seed Agnieszka Radwanska, who holds a 2-0 career head-to-head record over her second-round opponent.
Dominika Cibulkova, the 10th seed from Slovakia, battled past Canadian wildcard Francoise Abanda 6-1 3-6 6-0.
Czech 15th seed Lucie Safarova dismissed Romania's Sorana Cirstea 6-4 6-2 to progress, while qualifiers Heather Watson and Shelby Rogers continued their runs in Canada.
Briton Watson edged out fellow qualifier Tereza Smitkova of the Czech Republic 6-4 5-7 6-4, while American Rogers defeated Croatian wildcard Ajla Tomljanovic 6-4 7-6 (7-5).
Other qualifiers Lauren Davis and Kiki Bertens were not as fortunate, losing to Alize Cornet and Klara Koukalova respectively.
American Davis fell 6-3 7-5 to France's Cornet, while Dutchwoman Bertens was no match for Czech baseliner Koukalova 7-5 7-6 (7-5).
In terms of games won, Alison Riske of the USA copped the heaviest defeat of the day, as Slovakia's Magdalena Rybarikova ran out a 6-1 6-3 winner.