Tatar and Montreal native Marco Scandella earned assists on the goal. It was Scandella's first point as a Hab.
Tom Wilson evened things up for the Capitals on the power play with 90 seconds left in the first.
The teams headed to the room tied at 1-1 with Washington leading 12-9 in shots.
The Capitals took the lead early in the second. Just after Phillip Danault exited the box on a high-sticking penalty, Travis Boyd made it 2-1 for the visitors.
Jakub Vrana doubled Washington's lead at the 14:51 mark of the second.
Through 40 minutes of play, the Caps were leading 3-1 and outshot the Habs 16-9 in the middle frame.
With 14:51 left in regulation, Nick Suzuki sent a beautiful feed to Joel Armia, who thought he had Holtby beat. A video review, however, determined that the puck didn't completely cross the goal line and the score remained 3-1.
Suzuki succeeded with his next brilliant feed, though, sending it to Weise in the crease for the 10-year veteran to backhand it past Holtby and help him celebrate his 500th in style.
It was Weise's first goal of the season in Montreal.
Suzuki and Nick Cousins earned helpers on the tally, making it the third consecutive game in which Cousins has collected at least a point.
