Geelong were on track to run over the top of Carlton on Sunday after kicking the last two goals of the third quarter to reduce the margin to four points.
The Blues weathered attack after attack early in the fourth term, but with 10 minutes remaining Vescio produced a brilliant gut-running effort to turn the momentum back her team's way.
Amelia Velardo set up the foray forward after smothering an opponent's handball, but Vescio was 20m behind her opponent after the ball was kicked into space in attack.
Vescio put on the afterburners to catch Alexis Gregor holding the ball, before nailing the set shot.
Then with less than three minutes on the clock, Vescio shook off one opponent, gathered up her own soccer and handballed under pressure to set up Lila Keck to seal the 7.13 (55) to 5.7 (37) win.
The victory lifted Carlton (6-2) into fourth spot following Adelaide's shock loss to previously-winless Richmond earlier in the day.
"We're trying to keep a lid on it, we've got quite a few games to go," Carlton's Mimi Hill told the Seven Network after marking her 50-game milestone with a win.
"But it's pretty exciting to be 6-2, I've never had that in my time at Carlton. It's pretty special for 50 games."
Geelong are now 3-5 and face a huge battle to make the finals.
Abbie McKay (31 disposals, seven clearances), Hill (31 possessions, one goal) and Dayna Finn (26 disposals) led the way for Carlton, while Erone Fitzpatrick kicked two goals to go with her 24 disposals and 577m gained.
Vescio only finished with one goal from four disposals, but her final-quarter heroics proved crucial.
Amy McDonald racked up 25 possessions and six clearances for Geelong, while Aishling Moloney kicked two goals from 18 disposals.
Cats captain Meg McDonald, who was recalled following a four-week absence, was quiet with nine disposals.
Blues forward Tara Bohanna, playing her 50th game, kicked three behinds in the opening quarter, including one from three metres away which she slammed into the post.
Bohanna finally nailed her first major late in the second term with a 35m set shot on an angle - by far her toughest shot of the day - to extend the margin to 16 points.
Geelong made their move late in the third quarter.
Moloney worked her Irish magic to shake off an opponent and run into an open goal to keep them in touch, and the margin was just four points when Mikayla Bowen converted her set shot.
For Carlton to have such a slender lead at three-quarter time despite dominating the inside 50m count 41-19 was a big shock, but Vescio stood up when it mattered most to get the Blues over the line.
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