The Spaniard and the Aussie were meeting for the third time overall, but first time in Melbourne. Carrying the home advantage, Tomljanovic was looking to carve out her first win over Muguruza since 2014 - and she had plenty of support from the crowd while she was at it.
Tomljanovic had taken down Anastasija Sevastova in straight sets in the first round, allowing the Latvian just two games in total. Muguruza on the other hand had a slow start against Shelby Rogers which earned her a bagel in the first set, before she rebounded to win the next two sets 6-1, 6-1.
The Spaniard got broken in the very first game, but she broke back in the fourth. That marked the start of some stability for the former world number one as two more games put her ahead 4-2.
Muguruza kept up the pace and pushed through another service game to lead 5-2, with the set in reach. Tomljanovic denied her a break by holding to love, but Muguruza returned the favor to end the set in 47 minutes.
The Spaniard scored 70 percent from her first serve with 12 winners, and also committed two fewer unforced errors than Tomljanovic. Her forecourt game was working well too as she won nine of 11 points at the net.
The two managed service holds through five games in the second set before Tomljanovic got a window of opportunity when Muguruza committed an error on deuce. The Aussie worked hard for every point and finally got the break for a 4-2 lead.
Tomljanovic consolidated to reach 5-2, with a shot at forcing a decider. Muguruza denied her a break to extend the set, but Tomljanovic secured the hold of serve to win 6-3 in 48 minutes.
Muguruza still had the energy to fight in the deciding set and held to love in the first game. Tomljanovic nearly did the same but let the Spaniard get a point before closing the second.
The former world number one scored another love hold before adding a break for a 3-1 lead. The Australian answered with a break back before adding a hold that leveled them at three-all.
Muguruza edged Tomljanovic in the seventh game but halfway through the eighth umpire Marija Cicak halted play as the rain came pouring down. That necessitated the closing of the roof, and the lights came on too.
Muguruza kept up her charge after the resumption and got the break, which allowed her to serve for the match. The Australian then saved one match point with a winner and Muguruza squandered the second with an error, forcing deuce. But the Spaniard found that three was a charm as she put Tomljanovic away with a winner, completing the match in 2 hours and 21 minutes.
“It was a tough battle,” Muguruza said during her on-court interview. “We both fight until the end. I think Ajla played very well so I had to level out my game and stay in the fight until the last moment.”
Muguruza now awaits the winner of the match between world number six Elina Svitolina and American Lauren Davis.
Published 23 Jan 2020, 08:52 IST