Abraham Papali'i and Shane Delahunt were sent off in the second half and Munster capitalised to move into the last four of the Pro14.
The Ospreys were on the verge of victory despite George North's early red card, but Ashton Hewitt's try salvaged a draw for the Dragons.
Peter Robb's dismissal did not prevent Connacht from closing the gap to the Scarlets to only two points ahead of their clash on Friday.
Leinster became the first Pro14 side to win their first 12 league matches of a season after they overcame Ospreys on Friday.
The Ospreys claimed only their second Pro14 win over the season at the expense of high-flying Ulster in a stormy Swansea.
At the end of another week of crisis, Saracens had rare cause for cheer as they reached the quarter-finals of the European Champions Cup.
Rhys Carre's early red card made life difficult for Saracens, but they still defeated Ospreys in the European Champions Cup.
Ospreys were boosted by George North's return but still could not see off Dragons in Pro14.
George Turner's late try ensured Glasgow Warriors claimed the bragging rights in their 1872 Cup clash with Edinburgh in the Pro14.
Brothers Billy and Mako Vunipola played starring roles as reigning champions Saracens defeated Munster in the European Champions Cup.