While Abhishek got a trophy for the best comic role in "Bol Bachchan", Big B received a special award for being an iconic legend.
"Father son win awards at Screen... Abhishek best comedy role and yours truly for outcome of a poll an all India for iconic legend," Amitabh tweeted Sunday.
"There is pride, joy and gratefulness... How much effort is put in to reward talent and creativity," the 70-year-old posted.
The award ceremony took place Saturday night.
The evening saw off beat films "Paan Singh Tomar" and "Barfi!" winning top honours.
While both films shared the best movie award, Irrfan and Ranbir Kapoor, lead actors in the two films respectively, shared the best actor trophy.
Late filmmaker Yash Chopra, who died in October 2012, was conferred the lifetime achievement award at the gala.
The event was hosted by Shah Rukh Khan, Karan Johar and Ayushmann Khurrana, who bagged the best newcomer (male) award for his performance in "Vicky Donor".