There were tries for Alex Goode, Chris Wyles, Maro Itoje, Richard Wigglesworth and Schalk Brits, plus a penalty try and 13 points from the boot of Owen Farrell as the visitors eased to the victory.
Oyonnax's points came courtesy of a late try for replacement Arthur Aziza, a conversion from Regis Lespinas, and a penalty from Rory Clegg.
Saracens knew backing up their strong start with another win would put them in firm control of the pool at the halfway stage.
The English champions had only won three of their 10 Champions Cup pool games in France, but they had been victorious in the last two and they proved far too strong for a side sitting bottom of the French Top 14 table.
The pack took control early on, with lock Itoje making a couple of telling carries and helping to force an early penalty, only for Farrell to push his effort wide.
The England international made no mistake with his second attempt in the seventh minute as Saracens strength up front was again felt by their hosts.
The first try should have followed in the 17th minute. Farrell's drifting line fed Wyles into a gap and the American fed Chris Ashton on the outside, only for Silvere Tian to get back and make a crucial intervention.
But it proved a brief reprieve for the home side as from the resulting scrum Saracen got a nudge on and when Oyonnax scrum-half Fabien Cibray strayed offside to kick the ball away referee Marius Mitrea headed under the posts for a penalty try, converted by Farrell.
Oyonnax responded with a good spell and forced a succession of penalties, but fly-half Rory Clegg was off-target with his first two attempts, striking the post with the second.
However, the former Newcastle man did find his range with his third effort to get the hosts on the board in their first home fixture in top-tier European competition.
Having stuttered through the middle part of the half, Saracens finished it with two superb scores.
Firstly, Billy Vunipola's smart pass opened space for Farrell to break through, with Wyles feeding inside for Goode to step his man and score.
Then lovely handling between forwards and backs saw Will Fraser rampage into space to send Wyles racing over. Farrell converted both scores to leave the visitors in total control at the interval.
Oyonnax started the second half on the front foot, knowing an early score was crucial to give them any hope of an unlikely comeback.
But Saracens killed them off with two quickfire scores, the first coming as Marcelo Bosch's long pass found the overlap and Michael Rhodes sent Itoje cantering over for the crucial fourth try.
From the restart Sarries attacked again, Rhodes breaking the line. The flanker did not have the legs to go all the way and fed Wigglesworth for an easy finish.
Replacement Aziza got a late consolation for the hosts but Saracens had the last word through Brits.