The Lions were ahead by just three at halftime before their stars turned on the jets with a seven-goals-to-three third quarter to set up the 17.13 (115) to 12.8 (80) win on Sunday.
It gives Brisbane back-to-back victories ahead of their bye and blockbusters against Sydney and Geelong in the fortnight afterwards.
Will Ashcroft, who finished with a game-high 38 possessions, came to life early in the third term with two successive goals including a freak six-pointer dribbled in from the boundary line.
It was the 22-year-old's best disposal tally of the season, to go with eight clearances.
Lachie Neale put his stamp on the game early in the third period as Richmond failed to keep up after putting the defensive heat on Brisbane in the first half.
Despite conceding the Lions were still far from their best, Fagan said his team was tracking in the right direction.
"Fourteen games into the season with a long injury list, we're still eight wins and six losses," he said.
"Hopefully we can get a few players back and launch a bit of an attack in the second half of the year.
"We're not getting too carried away, but there's opportunity there if we're good enough.
"It's just been good the last couple of weeks, after losing three in a row.
"The main aim is to try to qualify for finals. You want to finish in the top four if you can, but sometimes just giving yourself a chance is the best thing you can do."
Ryan Lester, Henry Smith and Dan Annable are likely to be available for round 16 against Sydney, with bigger guns Dayne Zorko and Hugh McCluggage back in the weeks to follow.
Logan Morris picked up three goals for the Lions, forward Eric Hipwood booted two in his 200th game on return from a knee injury suffered in round 23 last year, and defender Harris Andrews took nine marks in his 250th.
Youngster Jasper Alger was a stand-out for Richmond with four goals, while team mate Tim Taranto was busy with 29 disposals and two goals.
Both teams went tit-for-tat in an engaging opening, with a fairly simple Bruce Reville goal close to the posts giving the Lions a 28-25 lead at quarter-time.
Richmond's Liam Fawcett had two goals for the term, while Brisbane's Zac Bailey had one for the highlight reel after walking the boundary line and finishing with a banana kick.
Second-last Richmond had the running early in the second term but missed multiple gettable shots, before Alger kicked his second to reduce the margin to two points.
Taranto put the Tigers ahead but Josh Dunkley kicked a crucial goal moments before halftime to put Brisbane back ahead 42-39.
From there, the Lions kicked 11 of the 17 second half goals.
Tigers' coach Adem Yze said he was proud of his side's effort after a 114-point drubbing against Sydney last start.
"We just weren't good enough in the end. Their execution was better than ours," he said.
"But the effort and the response, we felt we played the right way."
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