After captain Sairaj Bahutule (4-27) led the bowling attack to restrict the hosts to 152 in the first innings, India 'A' shrugged off a poor start to close the first day at 133 for three at Harare Sports Club.
The cheap dismissals of top three batsmen - Dhiraj Jadhav (6), Gautam Gambhir (5) and S Sriram (0) - brought Gavaskar and Karthik together at 26 for three and the pair batted solidly to set the team on course for a huge firstinnings lead.
Gavaskar (batting 57) and Karthik (52 not out) have so far added 107 runs for the unbroken fourth wicket stand.
Seamer T Panyangara did the early damage in the visitors' innings, claiming all the three wickets with some impressive bowling.
Earlier, put in to bat, the Select XI lost wickets at regular intervals to be bowled out for 152 in 58.1 overs.
Avishkar Salvi and S S Paul removed the openers before a double strike by Amit Bhandari reduced the hosts to 41 for four.
A 46-run partnership between Test players Mark Vermeulen (23) and M Matsikenyeri (28) stemmed the rot briefly before Bahutule and Romesh Powar (2-30) ripped through the line-up.
Select XI 152 all out in 58.1 overs (C Chibhabha 41, M Matsikenyeri 28, M Vermeulen 23; Bahutule 4-27, Powar 2-30, Bhandari 2-38) Vs India 'A' 133 for three in 31 overs (R Gavaskar batting 57, D Karthik batting 52; Panyangara 3-30).