Visiting Academica will have hoping for a win to move them closer to the European spots, but they struggled to break down their hosts, who had the better chances.
Braga dragged a good opening wide on the first half, while Rafael Lopes had Academica's best chance in the second half.
Nuno Lopes wanted a penalty for the hosts 64 minutes in, but referee Duarte Gomes waved away the wing-back's appeals.
Lopes' evening went from bad to worse in stoppage time as he was dismissed for a second bookable offence.
A point apiece leaves Academica six shy of the top five, though Rio Ave enjoy a eight-point cushion over the relegation zone.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.