Kerala resumed their first innings at 163 for 4 but were all out for 248 with Sachin Baby top-scoring with an agonisingly slow 61 which came from 209 balls.
None of the other Kerala batsmen could contribute with substantial scores.
Saxena then led the Kerala bowling charge to restrict Himachal to 198 for 8 at stumps.
Himachal now trail by 50 runs with two first innings wickets in hand.
Opener Prashant Chopra was the main contribute for Himachal with a 79-ball 60 while none of his colleagues could make a substantial contribution.
Kerala: 248 all out in 107.1 overs (Sachin Baby 61; Rishi Dhawan 4/66).
Himachal Pradesh: 198 for 8 in 56 overs (Prashant Chopra 60; Jalaj Saxena 5/53).
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