Webber's second-place finish moved him into third place in the championship, 4 points behind Hamilton in third, and nine ahead of Jenson Button, who was sixth in Turkey.
With Turkey being the first European race of the season, several teams introduced upgrades to their cars in order to aid with their respective performances on the grid.
Nico Hülkenberg substituted for Adrian Sutil at Force India, while Daniel Ricciardo drove in the place of Jaime Alguersuari at Scuderia Toro Rosso.
Jenson Button was third in the standings with 38 points, 1 ahead of Mark Webber who had scored his first podium of the year when he drove from 18th to 3rd in China, three weeks previously.
The second session was held in drying conditions, where Button was marginally quickest ahead of Rosberg, the only drivers to record a sub-1:27 lap time.
[13] Pastor Maldonado crashed his Williams into the barrier, having run wide on the exit of Turn 8, and spun out on a damp patch.
Virgin Racing's Jérôme d'Ambrosio later received a five-place grid penalty for ignoring yellow flags in the area of Maldonado's accident.
[14] The third session saw the top four places taken by the Red Bull and Mercedes cars; Vettel finishing as the fastest driver ahead of Schumacher by 0.001 seconds.
Webber was almost four tenths adrift in third, just edging out Rosberg in fourth, after recovering from a high-speed spin at Turn 8 during the session, while McLaren wound up fifth and sixth with Button getting the better of Hamilton.
[15] Maldonado and Sergio Pérez were next on the grid ahead of the Toro Rosso pair, with Sébastien Buemi getting the better of Jaime Alguersuari by three tenths.
Jenson Button qualified in sixth place for McLaren, followed by Vitaly Petrov in the Renault and Schumacher in the second Mercedes in eighth.