Koiki made the most of his opportunity to play in a more advanced role with the Clarets’ opening goal just before the break.
And following nine changes at half-time on a sweltering evening on the Fylde coast, substitute Wood tapped in his sixth goal of the pre-season schedule to double the lead with almost an hour gone.
Boss Sean Dyche gave 45 minutes to 19 of his outfield players, with only central defender Kevin Long having to put in an extended shift in the absence of Ben Mee and Ben Gibson, who are both nursing knocks.
Charlie Taylor was fit enough to make a welcome return for his first outing of the summer programme against the club where he previously enjoyed a promotion success during a loan spell from Leeds United.
And with Taylor starting at left-back, Koiki was pushed forward into the left-hand side of midfield.
Having missed an early chance – volleying wide at the far post from Matt Lowton’s fine swinging cross – the 19-year-old then enjoyed his big moment.
From the Clarets’ first corner of the game in the final minute of the first half, Koiki pounced after Matej Vydra’s shot had been blocked and on the turn struck a low left-footed shot through a crowd of bodies and into the bottom corner.
The goal came just after the tide had begun to turn Burnley’s way following a bright start from Fleetwood.
The League One side – managed by ex-Claret Joey Barton – carried the early threat and almost went in front in the first minute.
Giant defender Harry Souttar was a handful in the air and when he connected with a powerful header, it took a sharp block from Joe Hart to parry the ball away.
Hart handled well throughout a 90-minute appearance, although Town twice had chances after the break to beat the former England man through Conor McAleny and Souttar who both headed wide.
McAleny’s effort came seven minutes into the second half and shortly afterwards Burnley punished the lapse by going 2-0 up.
Josh Benson and Johann Berg Gudmundsson were both involved in driving the Clarets forward and when Phil Bardsley joined in from right-back, his low cross was perfectly delivered for the predatory Wood to side-foot home from inside the six-yard box.
A couple of moments of inspiration from Dwight McNeil hinted at more to come from the visitors as they attacked the goal in front of a full stand of travelling supporters.
But Koiki’s red-letter night and Wood’s usual contribution proved enough – along with a welcome clean sheet – as the Clarets grew in strength as the game went on to take another important step along the way to peaking for the real thing.
Fleetwood Town: Cairns; Coyle, Souttar; Clarke, Andrew; Rossiter; Burns (Hunter 60), Coutts, Biggins, Morris; McAleny. Substitutes used: Crellin, Sheron, Southam-Hales, Rydel, Saunders, Mooney, Hunter, Boyle, Baggley.
Burnley first half: Hart; Lowton, Tarkowski, Long, Taylor; Lennon, Hendrick, Westwood, Koiki; Vydra, Rodriguez.
Burnley second half: Hart, Bardsley, Long, Dunne, Pieters; Gudmundsson, Cork, Benson, McNeil; Wood, Barnes.