Chasing a target of 163, Bengal could only manage 136/9, thus losing their second game in four matches.
Bengal huffed and puffed their way to a tense three-wicket win over Haryana.
Saha is set to return to action for the first time since May 25.
Bengal pacer Ashok Dinda recently was struck on his forehead while attempting a difficult caught-and-bowled chance during a practice T20 match at Eden Gardens.
Bengal begin their Syed Mushtaq Ali T20 Trophy against Mizoram in their group D fixture at the Barabati Stadium in Cuttack on February 21.
The incident happened when batsman Birender Vivek Singh hit straight and Dinda attempted the catch on his follow through.
Both, Bengal and Punjab finished with 23 points to finish behind Madhya Pradesh (24) and Kerala (26), the only team to qualify.
Talented 19-year-old Shubman Gill (91) seized the initiative earlier in the day, hitting at brisk pace all around the ground with Anmolpreet playing second fiddle.
But the lanky left-hander Sidhu, playing only his second first-class match, batted with tremendous resolve as he rebuilt the innings with Shivam Sharma (42).
With the three points, Bengal have moved ahead of Hyderabad to fourth position with 15 points from five games.