In their first meeting with Ukrainian opposition, Leicester had to withstand a sharp start from their Group G rivals at the King Power Stadium on Thursday.
However, Maddison's 29th-minute effort put Brendan Rodgers' side ahead, with Barnes – who had played a crucial role in the opener – doubling the lead on the stroke of half-time.
Wesley Fofana missed a chance to make matters even more comfortable, though the points were wrapped up when Iheanacho slotted in a low finish.
Vladyslav Kabaev should have capped a dominant start for Zorya with an opener in the 22nd minute, only for the forward to fail to beat Kasper Schmeichel from close range.
Maddison saw a goal rightly disallowed for offside from the counter-attacking move that followed, but he broke the deadlock moments later.
Barnes' wonderful strike hit the post but Iheanacho managed to turn the rebound into the path of Maddison, who prodded into an empty net.
Leicester got lucky when Dmitriy Ivanisenya volleyed wide from Schmeichel's poor clearance, yet they had their second when Barnes raced onto Iheanacho's flick and lifted a sublime finish over Mykyta Shevchenko.
Fofana headed just wide 10 minutes after the restart, with Maddison then curling over from the egde of the penalty area.
A third for the hosts did eventually arrive in the 67th minute, Iheanacho – who became the first Nigerian to assist two goals in a single Europa League game – rounding off a fine individual display with a brilliant finish to add further gloss to the scoreline.
What does it mean? Foxes back to winning ways
Without the injured Jamie Vardy, Leicester went down 1-0 to Ross Barkley's late goal for Aston Villa on Sunday, following on from a 3-0 defeat to West Ham before the international break.
However, they bounced back from those disappointing results, securing their maiden win in UEFA's second-tier club competition, though they had only previously played in it during the 2000-01 season.
Leicester's front three run the show
Barnes was key to both of Leicester's first-half goals, while Maddison, who has scored twice in his last three appearances in all competitions, proved instrumental in a free role, having three shots and creating two chances.
Yet Iheanacho was arguably the star performer, with his persistence integral to Leicester's opener. He also displayed brilliant skill for the second, then dispatched his goal with pinpoint accuracy.
Kabaev left to rue glaring miss
Schmeichel rushed off his line to close the angle on Kabaev, but Zorya's striker should have done better from less than 10 yards out. It proved to be his only attempt of the game as he was taken off in the 65th minute.