Polec, who crossed from the Brisbane Lions at the end of last season, added pace and long kicking to the Power midfield while Justin Westhoff dominated in the forward line with five goals.
In a night that saw star Bombers Jobe Watson, Brendon Goddard and new recruit Paul Chapman play their first pre-season games, it was Port that controlled the match for longer periods, winning by 25 points: 1.11.15 (90) to 0.9.11 (65).
But it wasn't all good news for the Power, with key forward Jay Schulz helped from the ground with an ankle injury during the third quarter after opponent Michael Hurley fell across his right leg in a marking contest.
Bombers half-back Michel Hibberd, meanwhile, suffered what coach Mark Thompson said was a minor hamstring strain and was substituted out of the match before half-time.
Originally recruited with pick No.5 in the 2010 NAB AFL Draft, Polec showed why the Lions' recruiters were willing to invest such a prized selection in him, winning 23 possessions and kicking a brilliant supergoal.
Traded at the end of last season for pick No.34 in the 2013 NAB AFL Draft, having requested a move back to his home state, his pre-season performances suggest the Power will get a great return on their bargain investment.
"We're pretty happy with our decision with Jared, we're pretty pleased that he's playing for us," Power coach Ken Hinkley said.
"He knows that he's in an environment that will help him learn and keep him accountable to learning.
"That's not a reflection of where he's come from that's just a reflection of a young man maturing a little bit."
In a tall forward line that also included Schulz and John Butcher, Westhoff shone with five goals, including back-to-back goals after he was slung to ground after kicking the ball in the second quarter.
At the other end of the ground, young Bomber Joe Daniher played as his team's main forward target after Jake Carlisle was withdrawn from the squad of 29 before the match.
The 19-year-old made a bright start, kicking 1.2 with his first four possessions, but he had just one possession in the second half and lacked support, finishing with two goals.
Chapman moved between the forward line and midfield and was among his team's better performers, playing four quarters and finishing with a team-high 24 possessions and five inside 50s.
Goddard, meanwhile, was substituted into the match in the second quarter and came to life in the third, finishing with 16 possessions and a goal.
Essendon faces Richmond in a practice match at Punt Road Oval on March 7 while Port Adelaide will play St Kilda at Alberton on March 8.
WHAT WE LEARNED
Essendon: The presence of key tall Jake Carlisle is crucial for young forward Joe Daniher, who found himself overworked and without support against Port. The duo have worked extensively together this summer, forming a strong partnership. Working solo on Tuesday night, Daniher managed two goals but was often fighting two or three opponents.
Port Adelaide: After returning from a serious knee injury in brilliant fashion last season, Robbie Gray is ready to take his game up another peg in 2014. The midfielder/forward was influential on Tuesday night, playing without tape on the right knee for the first time since he twisted it against Collingwood in 2012. He finished with 27 possessions (10 contested).
Essendon: It was a quiet night for the baby Bombers, with versatile midfielder Martin Gleeson (16 possessions and three rebound 50s) perhaps the most involved of those yet to debut. After an impressive NAB Challenge debut, Zach Merrett (nine possessions) was quieter in his second pre-season game, while 21-year-old ruckman Fraser Thurlow played a minor role as support to Patrick Ryder.
Jarman Impey, who was recruited with pick No.21 in the 2013 NAB AFL Draft, continues to draw attention with his speed and composure with the ball. He had just four kicks before being substituted in the third quarter, but he made things happen. Defender Tom Clurey held his own with 14 possessions and 11 marks.
ESSENDON 0.3.8 0.4.10 0.8.11 0.9.11 (65)
PORT ADELAIDE 0.4.3 0.5.10 1.8.12 1.11.15 (90)
Port Adelaide: Polec
Essendon: Daniher 2, Goddard, Colyer, Hocking, Winderlich, Hardingham, Steinberg
Port Adelaide: Westhoff 5, Schulz 2, Gray, Monfries, Wingard, Butcher
Essendon: Heppell, Zaharakis, Chapman, Daniher
Port Adelaide: Polec, Westhoff, Gray, Wines, Pittard, Wingard
Essendon: Hibberd (hamstring)
Port Adelaide: Schulz (foot)
Essendon: Goddard replaced Ashby in the second quarter; Z Merrett replaced Hibberd in the second quarter; J Merrett replaced Winderlich in the fourth quarter
Port Adelaide: Hartlett replaced Moore in the second quarter; Wingard replaced Monfries in the second quarter; Broadbent replaced Impey in the third quarter; Moore replaced Schulz in the third quarter
Umpires: Ryan, Ryan, Harris
Official crowd: 8,022 at Etihad Stadium