Resuming on 157 on the second day of their first innings, Rao batted brilliantly to reach 200 runs not out before the Indians declared on 510.
But a depleted Kenyan side, which had made 116 in their first innings, were no-match to the opposition and were all out for 168, thus bringing an early end to the match.
Ravindu Shah top-scored with 44, but the opener, who played with a sore toe, could not produce his magic which has seen him set a first class record for Kenya by scoring 247 runs in the four-day game.
Middle order batsman Hitesh Modi and fast bowler Thomas Odoyo did not play due to injuries and may not be available for the final three-dayer starting on Wednesday.
The match will act as Kenya's last build-up for the ICC Champions Trophy in England in September.