Ujah scored from close range after the 36-year-old Pizarro, who had twice before played for Werder and is the Bundesliga's all-time top foreign scorer, flicked the ball past three defenders.
Zlatko Junuzovic made it 3-1 with the last kick of the game for his second goal of the match to lift Werder to seven points in sixth place.
Hoffenheim's new signing Eduardo Vargas had scored with his first Bundesliga touch to level at 1-1. The 2015 Copa America winner, who joined on a four-year deal last month, connected with a Steven Zuber pass in the 49th minute.
Junuzovic had volleyed the visitors ahead after sloppy defending on the stroke of halftime and the Austrian sealed their win with the last goal of the game.
Pizarro, a crowd favourite at Werder, had revived their attack after coming on in the 82nd minute and he launched their late charge.
Hoffenheim, still without a win this season, are in 15th place on one point.
Schalke 04 striker Klaas-Jan Huntelaar squandered a penalty but made amends when he scored the winner in their 2-1 victory over Mainz 05.
The Dutchman saw his fourth minute spot kick saved by Mainz's Loris Karius but the keeper could do nothing to stop a charging Huntelaar in the 61st after Yunus Malli had cancelled out Joel Matip's lead for Schalke.
Wasteful Schalke, who should have scored several more goals, move up to fifth on seven points with their second win of the season.
Borussia Dortmund made it four wins out of four games when they crushed Hanover 96 4-2 on Saturday with champions Bayern Munich, in second place, also maintaining their perfect start with a 2-1 win over battling Augsburg, courtesy of a late penalty by Thomas Mueller.
Third-placed VfL Wolfsburg are four points behind on eight after a goalless draw at promoted Ingolstadt.
(Reporting by Karolos Grohmann; editing by Clare Fallon and Pritha Sarkar)
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