The Cats kicked five goals to one in the final quarter of their 11.6 (72) to 6.9 (45) victory at GMHBA Stadium on Saturday.
A quick burst of three goals in as many minutes split open a tight game early in the fourth term and improved Geelong's record to 4-5.
Dan Lowther's side are still within reach of the top eight with three rounds left to play, while the Giants (2-7) are out of finals contention.
Prespakis shone with 23 disposals, eight clearances, six tackles and two goals in her milestone appearance.
"Georgie's game, particularly in the last quarter, was really important for us," Cats coach Lowther said.
"When it counted the most, (ruck Caitlin Tipping) and Georgie connected a few times and got the ball going in the right direction."
Chantal Mason kicked three goals and Aishling Moloney finished with two, while Mikayla Bowen (22 disposals, one goal) and Amy McDonald (19 touches, five clearances) were also prominent.
It was Geelong's first AFLW win over GWS after three previous attempts.
"To be able to fight through when they pushed us to the limit and finish really strong was really pleasing," Lowther said.
"It was a real good sign of maturity for the group. It should give us a really good head start into the next few weeks."
Prespakis was in the action from the outset and kicked the opening goal, helping the Cats to a 14-point lead at the first change.
The Giants returned fire with a breeze at their backs, levelling scores through Brodee Mowbray's second-quarter snap and briefly edging ahead when Tarni Evans slotted her second major.
GWS midfielder Rebecca Beeson led all ball-winners with 18 disposals midway through the third term when she was caught high by Rachel Kearns and temporarily forced off the field.
Geelong immediately kicked the next goal through Bowen and led by six points at the final change.
Moloney's brilliant final-quarter snap sparked the Cats, who kicked 20 points clear on the back of further goals from Mason and Kate Kenny in quick succession.
GWS never stopped fighting but Prespakis shut the gate with her second goal and Mason put the icing on the cake with her third.
Evans finished with three majors for the Giants, who were well served by Zarlie Goldsworthy (27 touches, seven clearances, one goal).
Beeson (24 disposals, six clearances) and Kaitlyn Shroj (23 touches) also fought hard in a losing cause.
Geelong next face West Coast in Perth on Friday night in a huge game for both sides' finals hopes, while the Giants host Fremantle on Saturday.
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