The visitors had Christian Lell and goalscorer Adrian Ramos sent off in a six-minute spell in the second half but were on the point of holding out for a 1-1 draw until Pizarro headed home at the far post in the 93rd minute
Ramos had given Hertha a fourth-minute lead and Pizarro levelled in the 23th minute as Werder went second in the table, two points behind leaders Bayern Munich.
Lukas Podolski set up one goal and scored the second to give Cologne a 2-0 win over Hoffenheim in Sunday's other game.
Promoted Hertha went ahead when Rafael's low cross picked out Colombia striker Ramos, who held off a defender's challenge and dinked his shot into the far corner.
Pizarro, the highest-ever scoring foreigner in the Bundesliga, levelled when he outjumped his marker at the far post to head in from Clemens Fritz's long cross from the left for the 146th Bundesliga goal of his career.
Hertha's troubles began in the 57th minute when Lell was sent off for a shocking and senseless late tackle deep in the Werder half.
Werder spent the rest of the game laying siege to the Hertha area although, apart from Pizarro's disallowed effort, they threatened little with Marko Arnautovic shooting high or wide every time he got within sight of goal.
Hertha, 12th with nine points, survived a flurry of corners and free-kicks and, incredibly, nearly snatched a winner when Rafael's shot was deflected over the crossbar on the break.
In the other game, Cologne, 10th with 10 points, went ahead in the 20th minute when Podolski was sent clear on the left and pulled a low ball back for Mato Jajalo to score with a shot which went between a defender's legs.
