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.
The Peruvian also had a goal disallowed in a 81st minute, a decision which caused Werder coach Thomas Schaaf to protest so much that he was also sent off.
Lukas Podolski set up one goal and scored the second to give Cologne a 2-0 win over Hoffenheim in Sunday's other game.
Bayern, who beat Bayer Leverkusen 3-0 on Saturday to chalk up their sixth successive league win, lead with 18 points from seven games, two ahead of Werder Bremen and Borussia Monchengladbach.
They are followed by Hoffenheim, Schalke 04 and Hanover 96 who are a further four points adrift.
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.
Ramos followed six minutes later when he was given a second yellow card for pushing an opponent.
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.
Their resistance ended when Pizarro was left unmarked at the far post at a corner and predictably took advantage to score his fifth goal of the season in the third minute of stoppage-time.
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.
Stripped of the captaincy before the start of the season by new coach Stale Solbakken, Podolski had a shot well saved by Tom Starke and then produced a brilliant piece of skill on the goal-line to set up another chance for his side.
Podolski was close with a long-range effort in the 52nd minute and was rewarded 12 minutes later, collecting an excellent through ball from Christian Eichner before fooling Starke with a clever dummy and slotting the ball home.
