Just 50 seconds had passed when Maicousel pounced on some forgettable home defending to run the ball into an empty net.
Chievo recovered from their early calamity to equalise through Sergio Pellissier after 13 minutes before Luca Rigoni claimed the match-winner just before half-time with a deflected strike.
Udinese had the best chances after the break and, while Dusan Basta hit the crossbar, Chievo held on.
The visitors rested Antonio Di Natale and it looked like they might get by without their veteran striker when they were 1-0 up in quick time.
Chievo's defence were complicit in the goal with Bostjan Cesar pressurised into making a poor backpass that Alessandro Bernardini failed to control and allow Maicousel the simplest of tasks to score.
The Flying Donkeys did not let the moment embarrass them into further mishap as they instead got on the front foot.
Ivan Radovanovic saw a well-hit effort saved before Bernardini shaved the post with a header from a corner.
Chievo were level soon after when Pellissier beat the offside trap and latched onto a clever Nicolas Frey assist to slide in an angled shot.
Udinese almost went behind moments later as Ivan Kelava made a double save to deny Alberto Paloschi and Alessio Sestu.
Chievo were deservedly ahead five minutes before half-time when Rigoni's fierce shot took a deflection off Danilo to loop over Kelava.
Di Natale was brought on shortly after half-time and soon forced a low save from Christian Puggione before Basta crashed his shot against the frame.
Di Natale threatened twice more but Puggione was comfortable on both occasions to usher in a first-up win.