The former Mumbaikar, Jaffer, smashed a superb 68 runs while Satish remained unbeaten on 81 as Vidarbha reached 172 for two in 72 overs.
When the stumps were drawn, Satish and skipper Subramanium Badrinath were at the crease with Vidarbha still trailing Karnataka by 178 runs with eight wickets in hand.
Satish showed lot of patience and grit to build a 117-run partnership for the second wicket and brought the team back on the track after they had lost their first wicket on three in the very first over of Abhimanyu Mithun.
The duo remained unseparated between lunch and tea, despite some loud appeals as the hosts went wicketless in the second session.
"There were some close calls, but things can go against us. Some things are not in our hands," Shreyas Gopal said.
In the very second over after tea, Jaffer trying to change gears ended up giving a catch at mid-on to Karun Nair off left-arm spinner Jagadeesh Suchith. The flamboyant former Indian opener cracked ten boundaries in his 120-ball 68 runs.
After the fall of Jaffer, Vidarbha tightened their screws and made it difficult for the visitors to score runs. Satish and captain Subramanium Badrinath also did not want to lose further wickets as they dug their heels to end the day on a positive note.
"After the fall of Wasim Bhai's wicket, it was really very difficult for us to score runs because of the close-in fielding. I and Badri decided to stay at the wicket and look for small partnerships to frustrate the home bowlers," said Satish, who could muster 52 runs after tea with Badrinath.
For Karnataka, Mithun and Suchith picked one wicket each and Vinay Kumar, S Aravind and Gopal -- all went wicketless.
Resuming their overnight score of 298-6, Karnataka were bundled out for 350 runs in 102.4 overs, after wicket-keeper batsman Chidambaram Gautam scored 30 and Vinay 22.
Vidarbha pacer Ravi Thakur ended the innings, taking four wickets.
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