The Power jumped from ninth to fifth spot on the ladder with a hard-fought 16.20 (116) to 11.9 (75) win on Saturday night at Adelaide Oval.
After a tight initial three quarters, the Power booted four goals to none in the final term.
"A fair bit of credit to Richmond, when they stay close...it builds a bit of belief," Port coach Ken Hinkley said.
"They were able to get the ball through us a little bit too easy at time.
"It was always going to take a bit of time...it took right until the end."
Port half-back Dan Houston was instrumental in the victory with 25 disposals and Dixon's scoring was supported by three goals from Mitch Georgiades and two from Willie Rioli.
Captain Connor Rozee (24 touches) also booted two majors, Brownlow medallist Ollie Wines (32 possessions) and ex-skipper Travis Boak (24, one goal) were prominent, and Jordon Sweet ruled the rucks.
The last-placed Tigers were brilliantly served by Daniel Rioli, who gathered 28 disposals and kicked two goals, and Rhyan Mansell slotted three goals.
Stalwart Dion Prestia (24 disposals, one goal), on-baller Jacob Hopper (25) and Jayden Short (23) were also busy but the Tigers remained anchored on the bottom with two wins.
Richmond veteran Prestia kicked the opening goal as the visitors started strongly but failed to cash in on the scoreboard.
The Tigers at one stage had 16 to six inside 50s but a late Willie Rioli goal gave Port, propelled by 21 disposals between ex-captains Wines and Boak, a 4.2 to 3.3 edge at quarter-time.
The teams then traded goals in the second stanza as the Power gained ascendancy but, like their opponents in the first term, failed to fully convert.
Port kicked 3.6 to 3.3 for the quarter and held an eight-point break at halftime despite the visitors boasting the two leading ball-winners to the break, Daniel Rioli (21 touches) and Prestia (18).
In the third term, Richmond snuck within one point when Rhyan Mansell slotted his third goal with a superb snap from a tight angle.
But the Power rallied with three goals in less than three minutes to create a 20-point advantage with five minutes remaining of the quarter.
The Tigers again rallied with two late goals and a Kamdyn McIntosh strike reduced their deficit to 10 points at three quarter-time.
In the last quarter, Port forward Dixon converted a set-shot early to sap Richmond's resistance - the Power kicking 4.8 to one point in the final term.
"We were really happy with the way we were tracking for three quarters," Richmond coach Adem Yze said.
"But we weren't happy with the way that we finished, we got smashed at clearance, smashed at inside 50s."
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