The midfielder popped up in 89th minute as Rob Page's side came from 2-0 down to claim a late victory against their League One rivals.
The Valiants were two goals behind when the first half came to end as an early Jon Taylor strike had the Posh in front before Aaron Williams put the home side in the driver's seat in the 41st minute.
But the visitors forged a spirited fightback which started with Byron Moore's goal four minutes into the second half. JJ Hooper then equalised in the 86th minute before Dodds netted the winner just three minutes later.
On Thursday, Dodds mentioned his former club Leicester when speaking of Vale's recent form which was extended to four games without defeat.
"All we're trying to do is win the next game and hopefully that'll stand us in good stead," he told BBC Radio Stoke.
"It is similar to what Leicester are doing. They're not talking about winning the Premier League, they're just going about their business.
“There's massive belief in us but if you look too far into the distance, you're tripping up from what's in front of you."
It was the 29 year-old's 5th league goal of the season, and a crucial one as it leaves the Stoke-on-Trent club just three points outside a play-off spot.
Dodds is somewhat of a fans favourite at Port Vale having appeared over 300 times since joining back in 2008.
Check out the highlights below and Dodds' goal from 1:38 -