The third day's play ended with Vidarbha reaching 195 for four.
At stumps, Satish was going strong on 71 while Akshay Wadkar was batting on 19.
Sreenath Aravind was the pick of the Karnataka bowlers, claiming two wickets.
The 83-run partnership for the fourth wicket between Satish and Wankhade ensured Vidarbha get some runs to defend. After losing in-form opener Faiz Fazal - the second highest run getter in Ranji trophy this season - for a duck, their innings was somewhat steadied by the experienced Wasim Jaffer (33).
Aravind was hitting the deck hard with his in-dippers, and they were troubling the batsmen a lot. The pressure finally paid off with the wicket of Jaffer.
Aravind got the most important wicket of Jaffer, who was looking set for a big one, and the batsman was clearly unhappy with the umpire's lbw decision.
Just before tea, Vidarbha were dealt a body blow when Wankhade holed out at mid-wicket, driving a Aravind delivery straight to Vinay Kumar.
The score at tea was 174 for four for a lead of 58. Earlier in the day, Karnataka were all out for 301 to take a vital first-innings lead of 116 runs.
Overnight batsmen Karun Nair and R Vinay Kumar could add only seven runs to the total. Karun was dismissed after playing a superb knock of 153.
Rajneesh Gurubani picked up five wickets while India pacer Umesh Yadav claimed four.
Vidarbha: 185 and 195/4 in 47 overs (Ganesh Satish 71) Karnataka 1st innings 301 all out in 100.5 overs (Karun Nair 153; Rajneesh Gurbani 5/94, Umesh Yadav 4/73
First Published: December 19, 2017, 7:05 PM IST