The Tigers led by 36 points midway through the third quarter before Fremantle booted six of the next seven goals to reduce the margin to seven points early in the final term.
With just under five minutes remaining, Fremantle defender Ethan Hughes thought he had closed the margin to four points with a spectacular solo effort, but the goal umpire indicated Nathan Broad may have touched it on the line.
Replays showed the ball seemingly going through Broad's hands untouched but the evidence wasn't sufficient enough for the goal review system to overturn the decision.
Richmond held firm in the dying minutes to secure the 12.13 (85) to 10.10 (70) win, keeping their faint finals hopes flickering.
Bolton was the star of the show, with the 24-year-old finishing with 33 disposals, six clearances, 11 inside 50s and 920m gained.
He also booted the final goal of the match in the dying seconds.
Tim Taranto (35 disposals, seven clearances, two goals) was also superb, while Jayden Short booted three goals from outside 50m to set the tone.
For Fremantle, Caleb Serong (31 disposals, nine clearances) and forward Jye Amiss (four goals) were influential, while Nat Fyfe (17 disposals, four clearances, one goal) and Michael Walters (two goals) played key roles in the fightback.
Richmond forward Rhyan Mansell could be in strife for a huge bump on James Aish that rattled the Fremantle winger and even knocked his headband off.
Jack Graham will also be sweating for his dump tackle on young Docker Matthew Johnson.
Fremantle failed to capitalise on their early dominance, and they were made to pay dearly as the Tigers booted the last four goals of the opening term.
The Tigers' lead was still 18 points when a downpour hit the stadium early in the second term.
Amiss defied the conditions to pluck a contested mark and kick his third goal of the match.
Fremantle's chances looked dead and buried when Richmond shot out to a 36-point lead midway through the third quarter.
But in a frenetic finish to the term, Fremantle booted four of the next five goals to trim the margin to a manageable 19 points at the final change.
Fyfe provided the highlight of the fightback when he nailed a goal from the pocket after gathering a bouncing ball from the ruck tap.
Goals to Walters and Amiss early in the final quarter set Fremantle up for what would have been a famous victory but Richmond held firm in important moments to seal the win.
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