The second seed for the WTA International hard-court event survived a spirited challenge from her Australian opponent, prevailing 7-6 (7-5) 2-6 7-5 after two hours and 45 minutes of action.
Peng got off to a torrid start against the eighth seed as Tomljanovic romped into a 5-1 lead early on.
The Chinese recovered well, however, claiming five of the next six games to force a tie-break which she eventually won on her fourth set point.
Tomljanovic was dominant once again at the start of the second set and raced 4-1 ahead.
This time the world number 69 made her advantage count, taking the match to a decider, but Peng claimed early control of the final set with a 4-0 lead and looked on course to romp to victory.
Another twist was forthcoming, however, with Peng wasting three match points in the ninth game before being forced to save four break points in the 12th.
She finally booked a semi-final meeting with Bencic, who overcame Hsieh Su-wei 6-4 4-6 6-2.
After falling 2-0 behind in the final set, third seed Bencic looked in danger of crashing out to her opponent from Chinese Taipei but she responded strongly and reeled off six successive games to take the win.
The other semi-final will be contested between Zheng Saisai and Alison Riske, after the pair came through against Sorana Cirstea and Varvara Lepchenko respectively.
Zheng got the better of Cirstea 6-4 2-6 6-1, while sixth seed Riske was the only woman to progress in straight sets, winning 7-6 (7-5) 6-3.
Lepchenko served for the first set twice, at 5-2 and 5-4, but Riske clawed her way back and took the tie-break before breaks at either end of the second saw her close out the win.