Verona collapsed in the second half for a 3-1 defeat to Premier League side Burnley, despite going in front.
The first period had ended goalless at Turf Moor, but fitness levels were inevitably different as the English season begins two weeks ahead of Serie A.
Jutkiewicz had a goal ruled offside almost immediately and blasted another chance over the bar, but Luca Toni had gone round Heaton when Mee dived in with a goalline clearance.
Heaton also needed a fine save on Juanito Gomez Taleb from point-blank range.
Verona took the lead straight after the restart, as Toni set up Greek international Lazaros Christodoulopoulos for a header on the rebound.
However, just 60 seconds later Taylor beat Rafael on an Ings assist.
Burnley started to pile on the pressure in the final half-hour, as Jutkiewicz nodded in a Mee cross and Wallace scored with a splendid free kick.
Rafael kept the scoreline down with two marvellous saves on Ings.
Burnley 3-1 Verona
Scorers: Christodoulopoulos 47 (V), Taylor 48 (B), Jutkiewicz 62 (B), Wallace 83 (B)
Burnley: Heaton; Trippier, Duff, Shackell, Mee; Taylor (Kightly 77), Marney, Jones, Arfield (Wallace 69); Jutkiewicz (Sordell 62), Ings
Verona: Rafael (Gollini 85); Martic (Rodriguez 62), Marques, Gonzalez, Agostini (Luna 62); Obbadi (Ionita 62), Tachtsidis (Donati 62), Hallfredsson (Valoti 78); Gomez Taleb (Nenè 62), Toni (Fares 87), Lazaros (Zampano 62)