Stosur had won her previous two clashes with McHale, but this was the first on grass. So far, her best WTA outings on grass have occurred at Eastbourne, where she is a three-time semifinalist. She is playing Birmingham for the first time since 2008.
McHale's best grass court result was a third round showing at Wimbledon in 2012. She re-entered the Top 50 this week for the first time since March 2013 and beat Anna Schmiedlova in straight sets in her opener here.
Stosur came out on fire, winning the first five games en route to a lopsided first set. She was pushed a bit more in the second set but from 2-1 down won five of the next six games for the 6-1, 6-3 triumph. Especially memorable was her service game at 3-2 in the second set, which consisted of four aces.
By The Numbers
Stosur made good of four of five break point opportunities, while saving the only one she faced on her serve. She also fired eight aces and won 21 of 27 points on her first serve.
"I got off to a very good start, which helped my confidence," Stosur said. "There were a couple of tricky moments in the second set but I got through those, and I'm happy to be able to get a straight set win."
Stosur squares off with fellow Australian Casey Dellacqua, who scored a second round victory over Varvara Lepchenko. Stosur has lost both of her previous encounters with Dellacqua, though they haven't played since 2003.