The Bombers, seeking a response to Saturday's humiliating 10-goal loss to Adelaide, trailed for most of Thursday night's scrappy game, let down by wasteful goal kicking, and were down by 11 early in the fourth quarter.
But Essendon, sparked by Nate Caddy and Isaac Kako, kicked four goals in a row to claim a 9.18 (72) to 8.12 (60) win in front of just 25,114 fans at Marvel Stadium.
In the process, Essendon (1-2) piled fresh pressure on the Power (1-2) and coach Ken Hinkley, in his final season before handing over to senior assistant coach Josh Carr.
While Caddy (two goals) and Kako - who Scott dubbed "Batman and Robin" - and debutant Saad El-Hawli had their moments, Essendon's midfield stood tall.
Skipper Zach Merrett (34 disposals), Sam Durham (28 touches), Xavier Duursma (29) and Dylan Shiel, back in the middle, all had plenty of the ball.
Maligned defender - and former boom recruit - Ben McKay received Bronx cheers from his own fans, especially early, but fought through the game.
The Bombers' defence stood up late when it counted, with Jordan Ridley, Zach Reid and McKay all having their moments.
"I mean, the criticism of the defence was warranted, because the opposition kicked 160 points last week," Scott said.
"I'm not interested in answering to criticism, I focus on the facts all the time, win, lose or draw and what we've got to work on.
"The most pleasing thing is after you have a disappointing performance, you get to choose how you respond to it. You can capitulate, it's all too hard, and the pressure's overwhelming, or you can respond.
"And I think that's a pretty good measure of character."
Hinkley lamented a lack of consistent output from his senior players, with Jason Horne-Francis and Connor Rozee particularly down on form.
"When the game was up for grabs, they dominated us in the contest," Hinkley said.
"The disappointing part of it is our key players, our better players, the ones who we needed to step up, they just weren't quite at that level all the way through the game."
Power forward Mitch Georgiades stood tall early with two first-quarter goals and impressive aerial work, including a big hanger in the second quarter.
Port's Jase Burgoyne (27 disposals) racked up plenty of the ball off half-back, while Ollie Wines (31 disposals) was tough, with support from Christian Moraes (27 touches), and Aliir Aliir fought hard down back.
The game was on a knife's edge for three quarters.
Port led by six at three-quarter time and early in the final term, Horne-Francis brilliantly snatched the ball out of the air with one hand then drilled a terrific running goal to extend the lead to 11.
Then, El-Hawli, freshly substituted into the game, sparked Essendon with a brilliant burst off half-back that ended with Nic Martin goaling.
Mason Redman levelled the scores with a thumping long bomb, before Caddy kicked two points to snatch the lead.
Then, Kako danced around the Power defence before hitting up Caddy to extend the lead to eight.
Draper booted his second and the Bombers held on.
Essendon have the bye, while Port Adelaide host St Kilda next Sunday.
