Richardson struck in consecutive balls in the fourth over of Thursday night's match to dismiss Tom Rogers (20) and Beau Webster, and he repeated the dose in the 14th over on the way to figures of 4-25.
The Stars' total of 135 was below par, and Scorchers captain Ashton Turner (53 off 26 balls) and opener Adam Lyth (35 off 30 balls) helped get the home side over the line with 15 balls to spare.
The result, in front of 27,752 fans, lifted the Perth Scorchers (4-1) to the top of the table, while the Stars (1-4) have now lost three in a row.
The Stars were in all sorts of trouble at 8-86 when Richardson bowled Luke Wood around his legs after having Nathan Coulter-Nile caught on the boundary.
But some handy late blows from Hilton Cartwright (36 off 32 balls) and tail-ender Trent Boult (23no off 16 balls) lifted the Stars to a defendable total.
Lyth entered the match under huge pressure to perform after posting scores of 4, 10, 7 and 4.
The Englishman made a bright start with two early boundaries and his knock proved crucial in helping set up the run chase.
His night was ended in the 12th over when a rising Marcus Stoinis delivery bobbled off his leg, chest, chin and arm before striking the stumps.
Turner, on the back of his match-winning 48no against the Strikers, struck six fours and three sixes against the Stars before holing out with just two more runs needed for victory.
The biggest hero of the night was Richardson, who had two chances to snare a hat-trick.
Nick Larkin blocked out the first attempt in the fourth over, and Richardson's second effort - a full toss - was easily bunted away by Boult in the 18th over.
Richardson, who snared 4-9 in the season opener, now has 12 wickets this campaign to sit behind only Adelaide Strikers paceman Henry Thornton (14 wickets).
Jason Behrendorff (2-22) and AJ Tye (2-24) also played key roles with the ball for the Scorchers.
Marcus Stoinis was out for 10 when he skied Tye to mid-off in the 10th over, continuing a worrying form slump for the powerful batter.
Stoinis has now posted scores of 0, 0, 4 and 10 this BBL season.
His back-to-back ducks to start his campaign came while he was battling COVID-19.
The 33-year-old was rested from the Boxing Day loss to the Sydney Sixers, and his return against the Scorchers lasted just 10 balls.
