Ford, who was named Aviva Premiership Player of the Month for November last week, notched three penalties before the interval as Nick Evans took the one chance to bag his own.
It was left for Joseph to make sure of the win and he did so in fine style with a solo score after the break.
As a clash between two of the Aviva Premiership's most in-form teams - neither side having lost since Round 5 - something was going to have to give.
And it was Bath who came out of the blocks the fastest, Quins being penalised for coming in at the side to hand Ford his first penalty on a plate - and he duly obliged.
More pressure at scrum-time eventually yielded another penalty on the 22-metre line and 20-year-old Ford kept a cool head to knock through again with just five minutes on the clock.
Quins had barely entered into Bath territory due to stellar work from the latter's pack, despite being shorn of England tight-head David Wilson through a calf injury in midweek.
Finally Chris Robshaw and company led a charge that ended up five metres away from the try-line but more ill-discipline cost Quins at the last.
But the visitors had sprung to life as on the quarter-hour mark only Matt Banahan foiled Tim Molenaar, who had a wide open Charlie Walker at his side.
Ford's kicking from hand was also proving a menace however, pinning Quins back deep into their own half - before returning to the kicking tee to bag his third of the afternoon.
Opposing fly-half Evans had so far not had the chance to kick his side onto the scoreboard but the veteran made no mistake when Bath were caught handling 33 metres out.
Just before half time the hosts once more overwhelmed Quins from the scrum and Ford was given the nod again, but uncharacteristically missed from a difficult angle.
There was still time before the break for Quins to find themselves a man down after Walker was yellow carded for a tip tackle on full-back Anthony Watson.
Joseph was a peripheral figure in the first half but the centre exploded to life early on in the second, jinking and weaving from midfield before finishing off a scintillating try.
Ford failed to add the extras and Bath nearly let Quins back into the match straight away through Horacio Agulla's hashed clearance.
However, the hosts survived as both teams started to go blow-for-blow without finding the killer touch to convert opportunities into points.
Bath nearly engineered a breakthrough as Dom Day was brought down at the line-out, but Ford was wayward with a penalty again from a tricky position.
The match was entering its final stages and Quins were battering at the door before being held up just shy of the try-line with three minutes to go.
It was Quins ball at the ensuing scrum but one last effort from the home side's pack drove them back, being awarded a penalty to snuff out any hope of a comeback.