Rangers came into this after suffering four defeats in a row in this competition, with victory vital to reignite European aspirations.
Early on, Braga looked every inch a side with nine points from their opening four games and sitting pretty in the table. They brought confidence having already defeated Celtic in Glasgow earlier in this competition.
Twice Jack Butland did superbly to deny Ricardo Horta, first with a stretching low save and then to block when the striker raced in on goal.
The opening half hour brought no shots on goal for Rangers but, gradually, they began to exert some influence in the final third.
Danilo weakly shot at the goalkeeper after Diomande played him in. Djeidi Gassama then appeared to be touched by Martinez in the box and went to ground. Nothing was given but the crowd anticipated something was coming.
The opportunity arrived when Fran Navarro's outstretched arm connected with the ball in the area and the video assistant referee (VAR) intervened and Tavernier did the rest from the penalty spot.
In doing so, he equalled former Rangers striker Ally McCoist's European goal mark of 21.
It got better for the Ibrox side when red mist descended on Zalazar. He nodded toward Raskin, connected faintly, and was ordered off after VAR got involved.
A badly-needed Europa League lifeline looked odds on, until Djiga gifted Braga a leveller.
From a throw in, he appeared to panic and flicked his header towards Martinez, who atoned for his earlier penalty concession by tapping home and leaving his side seventh in the standings, with Rangers 33rd of the 36 teams.
