Changes were needed after the break and a more patient tactic ultimately wore Liechtenstein down and allowed Andrea Belotti, Eder, Federico Bernardeschi and Manolo Gabbiadini - the latter trio featuring from the bench - to make it 5-0 and put the game to bed.
National team boss Giampiero Ventura, who oversaw an 8-0 victory over San Marino earlier in the worldwide break, set his team up to score a similar number of goals against lowly Liechtenstein.
Insigne then turned provider for Italy's second goal five minutes into the second half.
Italy may yet beat Spain to first place in the pool by collecting more points than the 2010 World Cup winners, but improving goal difference will also be key. Young midfielder Lorenzo Pellegrini made his debut.
Antonio Candreva crashed home a sweet volley in just the second minute, but the assistant referee incorrectly ruled that the Inter winger was offside.
Insigne twice warmed Jehle's gloves with nearly identical efforts before Juventus defender Giorgio Chiellini, earning his 92nd cap, headed Antonio Candreva's corner against travelling defender Robin Gubser on the goal-line. "The problem was not the number of opportunities as we created about seven or eight good ones, but in the second half we were better".
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At the start of the second half Italy pressed forward en masse again and Belotti scored a fine goal to infuse the Azzurri with fresh enthusiasm.
"The first half was a lesson which will help us for the next match which is the one against Spain in Madrid", Ventura told Rai Sport.
Federico Bernardeschi, another substitute, added the fourth with a long-range shot and Gabbiadini turned in Leonardo Spinazzolo's pass for his first global goal since 2015. "When you want to do things in a hurry without thinking you lose your way". The chances and goals came in a flurry.
"If we head to Spain trying to do things too quickly, we'll end up messing it up". This is what I meant when I spoke about patience, we'll remember this in Madrid.
Giampiero Ventura's men rarely had to get out of first gear against Liechtenstein, who lost their 10th consecutive World Cup qualifying match despite holding firm for 35 minutes in Udine.
"Football is a game".
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