Jovanovski came through in a tightly-contested encounter on Wednesday, emerging victorious 6-3 3-6 7-5.
Eighth seed Azarenka was playing in her first Grand Slam since returning from a foot injury that forced her to miss the French Open, but the Belarusian was made to pay for only converting three of her 16 break-point chances in the match.
Jovanovski struck the crucial blow at the end of a frenetic decider to book a third-round clash with Czech Tereza Smitkova, who beat American Coco Vandeweghe in straight sets.
Flavia Pennetta was another seed to succumb to a surprise defeat, the Italian landing just 59 per cent of first serves in a 6-4 7-6 (7-4) defeat to Lauren Davis of the USA.
Davis will now meet Peng Shuai in the third round after the Chinese hammered Maria Kirilenko of Russia 6-0 6-3.
It was otherwise a day of comfortable progress for the seeded players, with almost all of the grass court tournament's big hitters making it through.
Two-time grand slam champion and second seed Li Na racked up 33 winners in her 6-2 6-2 demolition of Austrian Yvonne Meusbuger, while 2011 champion Petra Kvitova needed just 55 minutes to thrash German Mona Barthel 6-2 6-0.
Kvitova's win sets up an enticing third-round meeting with five-time champion Venus Williams following the American's 7-6 (7-4) 6-1 success over Japan's Kurumi Nara.
Fourth seed Agnieszka Radwanska produced another stunning display of her grass-court pedigree as the Pole delivered a disciplined display, making only eight unforced errors in a 6-4 6-0 victory against Australian Casey Dellacqua.
There is now just one British woman, Heather Watson, left in the draw due to Caroline Wozniacki's comfortable 6-3 6-2 win over Naomi Broady.
Broady follows Tara Moore, defeated by Vera Zvonareva 6-4 6-7 (3-7) 9-7 in a first-round clash held over from Tuesday, in bowing out of the tournament.
Meanwhile, 10th seed Dominika Cibulkova came from behind to overcome Belgium Alison Van Uytvanck 3-6 6-3 8-6 in an enthralling clash that lasted two hours and 35 minutes.
Lucie Safarova of the Czech Republic will be Cibulkova's next opponent following her straight-sets win over Slovenia's Polona Hercog.
France's Caroline Garcia - conqueror of 14th seed Sara Errani in the first round - continued her progress by eliminating American Varvara Lepchenko 7-5 6-3, while Czech Barbora Zahlavova-Strycova dispatched Russia's Elena Vesnina 6-4 6-2.
There were also wins for Michelle Larcher de Brito, Ana Konjuh, Ekaterina Makarova and Zarina Diyas.