The Blues trailed by 13 points at half-time and threatened to run over the top of their less experienced opponents at Ikon Park on Sunday.
They kept the Power scoreless in the final term and Goss won a free kick for high contact from Kate Surman with just seconds left, giving her the chance to win the game.
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She took her kick from just inside the 50-metre arc as the siren sounded, but it did not make the distance.
The teams finished locked on 4.3 (27) apiece in a result that denied expansion side Port Adelaide their first win in the national competition.
It came after the Power suffered losses to West Coast and the Western Bulldogs in the opening two rounds of their debut season.
“It’s a very odd feeling when you do draw,” Power captain Erin Phillips told Fox Footy.
“I’m really proud of our group and we seem to keep building each week.
“In the two previous games our momentum was getting there and our game was getting there.
“It’s disappointing we couldn’t get over the line but it’s definitely progress.”
Carlton had three players celebrating their 50-game milestones – Elise O’Dea, Jessica Dal Pos and Breann Moody – and all kicked goals.
O’Dea gave them the perfect start with one of two Blues majors in the first quarter but Port Adelaide hit back with a stunning surge in the second term.
Jade De Melo kicked two goals as the Power piled on four in quick succession to hit the front before half-time.
Moody and Dal Pos kicked the only two goals of the second half to get Carlton within two points early in the final term.
Darcy Vescio and Vaomua Laloifi both had chances to put the Blues in front but scored behinds that were only enough to level the scores.
Captain Kerryn Peterson (21 disposals), Mimi Hill (19) and Abbie McKay (26) were among Carlton’s best.
Impressive 18-year-old midfielder Hannah Ewings (21 disposals) was outstanding for the Power, who were also well served by Angela Foley (14), Abbey Dowrick (14) and Phillips (13).
The draw was Carlton’s first since the inaugural AFLW season in 2017.