The hosts are 231 runs behind going into the final day.
Kenya made a shaky start to their reply after they lost two early wickets when Kennedy Obuya went in the first over and Hitesh Modi was clean bowled by Junaid Zia.
But Shah, ably assisted by Tikolo, steadied the innings to push Kenya's score to a respectable 264 for three in 56 overs before fading light forced a premature end to the day's action.
Shah battled well with a flurry of boundaries and rallied to make 124 before Raiz Afridi, who had bowled Obuya for two, returned to rip the Kenyan top order.
Tikolo remained unbeaten on 104, while Thomas Odoyo (8) was not out at the close of play.