The 22-year-old Lisicki, who lifted her world ranking from 218 to 15 in 2011 as she recovered from an ankle injury, struggled to assert her powerful service game before beating Razzano in 85 minutes.
"It's always tough to play the first match of the season," Lisicki said. "I was struggling a little with my serve but that means there is still a bit to work on and improve, which is a good thing."
Lisicki gained control of the first set with an early service break and rallied from a break down to win the second set in 41 minutes.
"I've never played her, but I think it will be a great match for me," Barthel said.
Barthel, ranked 69, squandered several set points before taking the first set from the 67th-ranked Dokic, who made 32 unforced errors. She broke Dokic in the opening game of the second set, dropped serve then reeled off five straight games to win a match that finished just after midnight.
"It was very difficult, it's very late, but I'm just happy with the way I played," Barthel said.