Italian Errani is the highest seeded player left in the tournament after compatriot Flavia Pennetta withdrew with an injured ankle on Monday.
The 27-year-old showcased her talent by easily dispatching of qualifier Katerina Siniakova in a 6-3 6-2 win at the WTA International clay-court event in Austria on Tuesday.
Errani successfully landed 83 per cent of her first serves and showed solid defence to fend off five of the six break-point chances Siniakova had.
Argentina's Paula Ormaechea is her second-round opponent following her 6-3 4-6 6-3 success over Jovana Jaksic.
Meusburger's solitary WTA title came in the 2013 tournament and the sixth seed had to dig deep to ensure her defence lasted more than one round in a 7-6 (11-9) 4-6 7-5 win over Tereza Smitkova.
The Austrian won just 52 per cent of first-serve points and surrendered serve on eight occasions, but she dug deep to secure the win.
Carla Suarez Navarro, seeded third, also needed three sets to defeat qualifier Laura Siegemund 7-6 (7-3) 1-6 6-4.
Andrea Petkovic was the victor in 2009 and the German began her quest for a second title with a battling 7-6 (10-8) 7-5 win over Jana Cepelova.
Compatriot Dinah Pfizenmaier awaits in the second round, as she surprised Maria-Teresa Torro-Flor with a 6-7 (5-7) 6-1 6-4 triumph.
Some 65 spots separate the two in the world rankings, but Pfizenmaier fired down six aces on her way to victory.
Elina Svitolina and Camila Giorgi, the fifth and seventh seeds, also progressed. The former defeated home-favourite Patricia Mayr-Achleitner, while the latter ousted last year's runner-up Andrea Hlavackova.
Grace Min was due to face Pennetta on Monday before her withdrawal. And Min subsequently cruised to a 6-3 6-2 win over lucky loser Beatriz Garcia Vidagany.
Chanelle Scheepers was equally comfortable in a 6-1 6-2 success over Mariana Duque-Marino.
American qualifiers Irina Falconi and Shelby Rogers shocked Johanna Larsson and Kristyna Pliskova respectively to earn a spot in round two, while fellow qualifier Ana Bogdan was leading 6-3 3-0 before her opponent Ajla Tomljanovic retired.