Italy skipper Sergio Parisse has warned his side could be punished by the All Blacks.
Tonga trailed Italy 2-1 from their three previous encounters but the Pacific Islanders braved the cold and wet conditions to dominate the first half and came fighting back late on at the Stadio Mario Rigamonti.
Italy, who had left several regular starters on the bench and handed Tomasso Iannone his full debut at right wing, came out stronger after the break and ultimately prevailed thanks to a late penalty try.
But a week before hosting the world's greatest team at the Olympic Stadium, Italy gave little indication that they could cause an upset this coming Saturday.
Parisse, who was yellow carded in the first half - giving Tonga a chance to score their first try thanks to prop Alisona Taumalolo - admitted they can not afford a similar performance next week.
"The most important thing was the victory," said Parisse. "But at the end of the game I felt we hadn't done everything we'd set out to do.
"It's an important week for us, we'll regroup and train for next week in calm conditions but we can't play like that for 80 minutes against the All Blacks."
Azzurri coach Jacques Brunel said before the first of three autumn internationals - Italy host Australia in a fortnight in Florence - the pressure was off his side.
But Tonga came to perform, and did so in a dominant first half.
The visitors took a third-minute lead when Fangatapu 'Apikotoa sent a penalty between the posts, only for Lorenzo Cittadini to push over for Italy's opening try in the sixth minute.
Tonga eventually trailed Italy 18-16 at the break after the Azzurri helped push Leonardo Ghiraldini over to level the scores, with Burton adding two points from the conversion.
Italy re-emerged with more purpose but several promising offensives came to nothing and on other occasions they were guilty of giving ball away too easily while in try-scoring positions.
A Burton penalty goal took the hosts' lead to 21-16 in the 52nd minute, and on the hour mark both sides made a series of substitutions.
Martin Castrogiovanni's arrival made an almost immediate impact for Italy and the hosts extended their lead with a penalty try on 63 minutes.
Burton converted to take Italy to 28 points, but a defiant Tonga scored a try through Fetu'u Vainikolo after a good run on the left and 'Apikotoa took the scores to 28-23 after converting.
Prior to the start the Tongans' Sipi Tau war dance warned Italy of what was to come, and afterwards Italy coach Jacques Brunel was quick to highlight the Pacific Islanders' credentials.
"You can't forget, Tonga have beaten France and have put New Zealand in difficulty in the past," said the Frenchman.
But even before having to face the All Blacks' more fear-inducing Haka, Brunel and his Azzurri know they are in for a stiffer test.
"We can do better, we know that, but we don't see this as a negative result," Brunel said. "Maybe we didn't play our best rugby but if we could win every time we play ugly it would be nice.
"It's always difficult to get the engine running the way you want it to at the start of international series.
"We made a few mistakes but these are things we'll be looking to rectify in the coming weeks."
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