After a disappointing campaign on the clay, Davis ensured she made a bright start on grass, overcoming Tomljanovic's big hitting and a rain delay to edge through, 4-6, 7-6(1), 7-5.
"It was really tough - she was playing really well. I had a slow start and lots of errors and double faults, but I turned it round and kept believing." Davis said. "I really loosened up, cut down the errors and by the end I was playing really well."
Although a well-established stop-off on the ITF Circuit, this is Nottingham's first year as a WTA event and Davis enjoyed her first outing on Centre Court. "It's really nice, it's beautiful, the court was great. Of course it's early in the week so it wasn't too worn down yet," she added.
With Davis a couple of points from defeat in the second set, the British weather decided to ratchet the tension up another knot. "When it rained it got a little slippery, but it dried quickly and the crowd was great.
"I think we were both pretty nervous because it was a crucial point - I was down 5-4 and it was 30-30 - and I think the rain delay may have made her think a little bit because she missed her return. So maybe it worked in my favor."
Tomljanovic was not the only seed to fall by the wayside on the opening day. No.4 seed Karin Knapp also found the switch from clay to grass problematic, slipping to a 6-4, 6-2 defeat at the hands of Yanina Wickmayer. Elsewhere, there were wins for Bojana Jovanovski, Mirjana Lucic-Baroni and WTA Rising Star Ana Konjuh.
At 17, Konjuh is the youngest player in the draw by three years, but she belied her tender years to swat aside Shelby Rogers, 6-0, 6-3 in just 49 minutes. In the second round she will face either Sesil Karatantcheva or No.6 seed Casey Dellacqua.