The Durham batsman picked up two late wickets to put the Scots back in a strong position after the Kenyans had staged a spirited fightback at the Gymkhana Ground in Nairobi.
Scotland went into the third day with a lead of 185 runs and with high hopes of forcing an innings victory yesterday.
However, by the close it was the Africans who were 73 runs ahead after the Scots toiled all day in the searing heat.
Their main-line bowlers had managed just four wickets between them in the opening two-and-a-half sessions until skipper Gordon Drummond tossed the ball to Coetzer.
The Durham star responded by claiming his first two senior international scalps to leave his side needing just three more wickets before mounting their run-chase today.
However, they will face stern resistance from the obdurate Maurice Ouma who is unbeaten on 106.
Saltires coach Pete Steindl commented: "Kyle's two wickets were very important because it had been a really tough day for the lads.
"It was hot and there was not much help from the wicket which is low and slow.
"But we knew Kenya would come out fighting after being out for just 91 in the first innings."
Steindl added: "It was always going to be tougher for us the second time around because lightning rarely strikes twice in the same place. We always knew Kyle gave us another option because he was back bowling at the end of last season and he has the ability to move the ball both ways.
"It was worth a punt giving him a go and it has worked well."
Steindl, though, knows his side need to mop up the Kenyan tail quickly to avoid the target getting out of reach.
The day started promisingly for Scotland with Dewald Nel removing Rakep Patel and Majid Haq accounting for both Collins Obuya and Steve Tikolo.
However nightwatchman Hiren Varaiya defied the Scots for a marathon 237 balls, scoring just 44 runs before he was trapped by Nel.
Varaiya and Ouma managed to keep Scotland at bay for 28 overs as they searched for the fifth wicket.
Coetzer then joined the attack to clean bowl Jimmy Kamande and Nehamiah Odhiambo in a nine-over spell that brought 2-16.
However, Ouma, who has already hit 19 fours and a six in his unbeaten century, stands between Scotland and outright victory.
Steindl added: "It's important that our bowlers get the ball in the right areas from the start and that we take our chances when they come."