In pursuit of 251 for victory, Derbyshire got to the target comfortably, with Billy Godleman scoring an unbeaten 104 and Pujara left stranded ten short of what could have been his maiden County championship ton, after 105 balls and 121 minutes at the crease during which he hit 14 fours.
The victory was Derbyshire’s fourth in their last five championship games.
Looking to find his touch after a not-too-good showing on India's recent tour of England, Pujara, who failed in the club’s previous match against Glamorgan registering seven and a duck on debut, finally came good as Derbyshire reached their target at 251-2 from 66.4 overs.
Godleman and Pujara were involved in an unfinished third-wicket stand of 154 runs. They came together following the dismissal of Ben Slater, who along with Godleman, gave the side a solid start, putting on 94 in the first session, before Surrey could breakthrough.
Slater, on 45, was caught at first slip off Jade Dernbach at 94-1 in the third over after lunch after facing 106 balls and hitting five fours.
They suffered another hiccup in the following over as Wayne Madsen was caught at slip off left-arm spinner Zafar Ansari for 2.
However, Pujara stepped in at 97-2 and with Godleman saw the side through.
Image: Cheteshwar Pujara