Needing a win to overtake leaders Bayern Munich, Schalke fell behind to an opportunist goal from Ruud van Nistelrooy five minutes before half time, the Dutchman's third in the Bundesliga since his move from Real Madrid.
Kevin Kuranyi levelled just after the hour with his 15th league goal of the season and Ivan Rakitic put Schalke ahead with a twice-taken penalty, only for Burkina Faso forward Pitroipa to level with 13 minutes left.
Schalke were the only top three team to pick up a point at the weekend. Bayern were beaten 2-1 at Eintracht Frankfurt on Saturday, ending an unbeaten 19-match run in the league, and third-placed Bayer Leverkusen lost 3-0 at Dortmund.
Bayern stayed top with 56 points from 27 games but their lead over Schalke was cut to one point. Leverkusen are third with 53 points.
Schalke visit Leverkusen next week and host Bayern the week after that.
Injury-plagued Hamburg, who have been inconsistent during the season, went ahead against the run of play when Piotr Trochowski's free-kick was punched away by Manuel Neuer but landed at the feet of Van Nistelrooy and the former Manchester United and Real Madrid player fired in a right-foot shot.
Kuranyi, who has not played for Germany since walking out on the squad 18 months ago, headed Schalke level in the 62nd minute from Alexander Baumjohann's cross.
The Brazilian-born striker joined Borussia Dortmund's Lucas Barrios on 15 goals, one behind topscorer Stefan Kiessling of Leverkusen.
Six minutes later, Baumjohann was fouled in the area by Van Nisterlrooy and, after Rakitic's first penalty was disallowed for encroachment, the Croatia striker kept his cool and scored again at the second attempt.
The drama was not over as Trochowski burst into the Schalke area and found Pitroipa, who scored at the far post after only six minutes on the pitch.
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