Shakhtar top Gunners' group
Second-half goals by Razvan Rat and Luiz Adriano secured victory and ended Braga's hopes of also progressing.
Rat struck after 78 minutes at the Donbass Arena and Adriano sealed Shakhtar's fifth win from six group games with a second goal five minutes later.
Shakhtar finished with 15 points, three more than Arsenal who join them in the last 16. Braga take a Europa League place.
Chances were few for both sides in an uneventful first half.
Adriano fired wastefully over after 34 minutes and Luis Aguiar blasted wide for Braga after Shakhtar goalkeeper Andriy Pyatov pushed away a cross from the right flank.
But after the break, Shakhtar began to stamp their authority in midfield forcing Braga into several fouls and reducing the Portuguese side into trying speculative long-range shots.
Rat broke the deadlock when he gained possession on the edge of the penalty area after a pass from Darijo Srna and rifled the ball past Braga keeper Artur.
The Romanian then turned creator for the second, crossing for an unmarked Adriano to tap in.