Arriving at the crease with the Ranji Trophy champions left with only one recognised batsman, Kartik hit an unbeaten 89, his career best first-class score, to pull the hosts outof trouble.
At stumps, Railways were 235 for six, a lead of 12 runs that at one stage looked improbable after the Rest had reduced them to 106 for six soon after lunch.
Accompanying Kartik at the other end was the seasoned Yere Goud on 43 not out.
Goud's dour knock of 193 balls from 247 minutes with four fours was in contrast to Kartik's approach.
The left-hander struck 13 fours and a six during his 198 minute stay at the crease during when he faced 135 balls.
His effortless performance also made batting look easy on a wicket of uneven bounce that had consumed the top order inside the morning session.
Ramesh Powar did the damage with four for 78 but left-arm orthodox R Ramkumar was effective with none for 29 from 16 overs.
The other impressive bowling performance of the day was that of right arm seamer S Sreesanth with two for 35.
But the spectacled Kerala player blotted the scoresheet himself after stepping on the danger area on the follow through thrice from the same end and was ordered out of theattack for the innings.