The top seed looked set to cruise through after taking the opening set, but Gulbis fought back in the next two sets and, despite wasting six previous match points, the world number 40 eventually went through 2-6 6-1 7-5 in a match littered with unforced errors.
Second-seeded Jelena Jankovic and sixth seed Ana Ivanovic set up an all-Serb clash.
Elsewhere, sixth seed Anna Chakvetadze set up an enticing third round meeting with fellow Russian Maria Kirilenko by beating Alisa Kleybanova 6-3 6-4.
Tenth seed Richard Gasquet set up a last-16 clash with world No. 6 Tomas Berdych, while fellow Frenchman Gilles Simon will take on big-serving South African Kevin Anderson.
Meanwhile, Munich Open winner Mikhail Youzhny made an early exit to Latvian Ernest Gulbis 7-6 6-4 and 15th seed Stanislas Wawrinka set up a third-round showdown with world number one and Swiss compatriot Roger Federer after beating Leonardo Mayer, who was down 6-4 4-2 when he retired.
Fifth seed Ivanovic squandered a 4-0 lead in the third set, as 10th seed Radwanska reeled off six games in a row to reach the quarterfinals with a 6-1 3-6 6-4 victory.
The 21st seed came from one set down to beat the Serbian 1-6 7-5 6-3.
And if we're successful, then I think it becomes the seed of a broader set of agreements.
The Belgian second seed won the first set in 18 minutes but trailed 4-0 in the second before hitting back to set up a match with Australian Sally Peers.
In the men's draw, world No. 1 Novak Djokovic survived a late rally from Spanish fifth seed David Ferrer to set up a Friday semifinal with Argentine No. 21 Juan Monaco .
Murray, who had not dropped a set in reaching the last four, started as a strong favorite for the night match on Rod Laver Arena, but was second best to the 14th seed in the opening set.
Henin won the first set easily but Jankovic took advantage of Henin's fragile serve to level, only for the top seed to win a tense deciding set.
After his defeat, he said even taking a set off third seed Grosjean was a real morale-booster.
Spadea's fellow American, eighth-seed Mardy Fish dropped a set against Lee Hyung-taik of South Korea before winning 6-4 3-6 6-1.
Elsewhere, third seed Novak Djokovic saved two set points against Juan Monaco on his way to a 6-3 7-5 victory.
Henman was helped by a controversial over-rule from the umpire while facing break point at 4-4 in the opening set against ninth seed Lee.
There were five consecutive breaks of serve in the first set before 14th seed Clijsters established her authority to clinch it 6-4 after 52 minutes.
Second seed Clijsters won the opening set after breaking to take a 4-2 lead and then broke serve again to go 2-1 up in the second.
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Third seed Robin Soderling beat Nicolas Almagro 7-5 4-6 6-3 to set up a clash with eighth seed David Ferrer, who beat Lu Yen-hsun 6-3 3-6 6-1.
Italian second seed Francesca Schiavone came from a set down to beat Bulgarian Tsvetana Pironkova 3-6 6-3 6-1.
Elsewhere, eighth seed Anastasia Myskina lost the first set but fought back to beat Swiss player Emmanuelle Gagliardi 5-7 6-2 6-0.
Falla, the world number 60, served for the match at 5-4 in the fourth set, but top seed Federer dug deep.
Eighth seed Soderling blew a two-set lead as he crashed out, losing 5-7 2-6 6-4 6-4 6-2 to young Spaniard Marcel Granollers.
In the women's draw, top seed Victoria Azarenka came from a set down to beat Belgian No. 28 Kirsten Flipkens 3-6 6-3 6-0.
Rising star Golding lost the first set to the ninth seed but dug deep to claim a 4-6 6-4 6-4 victory on Court 12.
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On their return, and with both going off again in the middle of the second set, the 13th seed Ferrer won just three more games.
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Eighth seed Lopez edged the first-set tie-break before making the vital break in the ninth game of the second and served out for the match.
Fourth seed Williams breezed through the opening set in just 37 minutes after losing her first service game, and showed no signs of rustiness after her lay-off.
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