Iwobi made his first appearance of the season in the victory over West Bromwich Albion at the weekend but made the starting XI this time.
Everton did not let their guard down on Wednesday with Richarlison giving them the lead in the 22nd minute, courtesy of Bernard's assist.
The Nigeria international turned provider for the Toffees second goal, playing a lovely backheel to Richarlison after a brilliant one-two with the Brazilian.
1 - Alex Iwobi has both scored and assisted a goal in the same match for the first time in what is his 180th senior appearance in English football. Busy.— OptaJoe (@OptaJoe) September 23, 2020
Fleetwood were not going to give up so easily and pulled one back through second-half substitute Mark Duffy two minutes after the restart.
Everton would go on to extend their lead not too long after, thanks to Iwobi, with the Nigerian tapping home with consummate ease after being fed by Richarlison. It marked the first time the Arsenal academy graduate scored and assisted in the same match for the first time in his club career.
Fleetwood again cut the deficit, this time from Callum Camps in the 58th minute, but Everton were equally in the mood to get more goals and added a fourth through Bernard and substitute Moise Kean wrapping things up in added time with the fifth.
The victory will see Everton face West Ham United in the Carabao Cup fourth round at Goodison Park next week.
Iwobi had a brilliant evening, recording a total of five shots, four successful dribbles from seven attempts, 78 touches on the ball and 48 completed passes from 54 with an accuracy of 89%
The Super Eagles star played 25 times in all competitions last season having joined from Arsenal, scoring two goals and providing one assist.
The 24-year-old will hope to make his first Premier League start this season when Everton battle Crystal Palace at Selhurst Park on Saturday.
The Toffees kicked off their campaign first with a 1-0 Premier League win at Tottenham Hotspur followed by a 3-0 triumph over Salford City in the second round of the League Cup.
The next was an emphatic 5-2 win over newly-promoted West Bromwich Albion in the league on Saturday.