Saurashtra were 213 for seven with Sandip Maniar giving company to Makvana at the crease on 18 at close at the K L Saini Stadium at Mansarovar.
Makvana has so far faced 104 balls for his unbeaten 54 which he made with the help of five boundaries.
India Test player Chteshwar Pujara could score just three runs from 15 balls as Saurashtra struggled initially.
The visitors are still 86 run behind with three first innings wickets in hand.
Rituraj Singh (3 for 53) and Pankaj Singh (2 for 54) were the most successful bowlers for Rajasthan while Sumit Mathur and Saurabh Chouhan grabbed one wicket each.
Earlier, Rajasthan resumed at overnight score of 268 for nine were all out for 299 as their first innings folded with the fall of Dishant Yagnik (46).
In reply, Saurashtra were in deep trouble as Pankaj and Rituraj produced a fine spell to share four wickets to have the visitors reeling at 18 for four.
With Sagar Jogiyani (2), Shitanshu Kotak (1), Pujara (3) and skipper Jaidev Shah (12) back in pavilion, the hosts were right on top as Saurashtra went for lunch at 54 for four.
S P Jackon (54, 96 balls, 8X4) and A V Vasavdev (30, 75 balls, 5x4)) added 57 runs for the fifth wicket to steady the innings. But at the tea break, Saurashtra were struggling at 141 for 7.
It was Makvana and Maniar who kept the hopes of the visitors alive with their 72-run unbroken partnership for the eighth wicket.
