The Liverpool forward opened the scoring after eight minutes following a frantic beginning to the match before Moise Kean levelled just before half-time.
Solanke scored what would prove to be the winner at the beginning of the second half for the Young Lions, who are set to travel to Esberg on Tuesday to play Denmark ahead of next Friday's Euro 2019 draw in Bologna.
Nicolo Zaniolo gave the visitors two sizeable let-offs in the first couple of minutes, first rifling over from point-blank range before his next effort from even closer was somehow tipped away by Dean Henderson.
England were then forced into a fourth minute change as Jake Clarke-Salter's ankle injury meant he gave way to Brentford defender Lloyd Kelly, on for his debut at the age-level.
Italy then paid for their early profligacy as Solanke ghosted in-between Italy's centre-backs Filippo Romagna and Alessandro Bastoni to head home at the near post from Ryan Sessegnon's left-wing cross in the eighth minute.
In a frenetic opening, only Kean's heavy first touch prevented him from going clean through as England were given another warning of Italy's attacking threat.
Solanke was booked for a heavy challenge on Arturo Calabresi, who was introduced off the bench following an injury to Claud Adjapong midway through the first half.
Demarai Gray ended a fine individual run with a toe poke that was well held by Italy goalkeeper Emil Audero while at the other end England were pegged back three minutes before half-time.
The dangerous Vittorio Parigini whipped in a cross from the right flank which was met by a powerful header from Kean at the back post.
England came within inches of retaking the lead before the interval as Lewis Cook's speculative strike from distance was fantastically tipped on to the bar by Audero before bouncing over.
Henderson made a similarly excellent save to keep out Rolando Mandragora's thumping effort.
Solanke, perhaps a touch fortunate to still be on the pitch, put England ahead once again in the 53rd minute.
Jay Dasilva somehow managed to get his left-wing cross into the area and some poor defending from Italy allowed Solanke to tap in.
Cook and Sessegnon were both off-target with their efforts as England sought to give themselves some breathing room before both sides made a spate of substitutions after the hour mark.
Tammy Abraham, introduced in the 69th minute, made a strong impact and forced Audero into action as the game entered the final quarter of an hour.
Italy, though, pushed hard for an equaliser in the closing stages and only an excellent reflex stop from Henderson kept out Patrick Cutrone's close-range effort.
England, though, survived a few late nervy moments to record a morale-boosting victory.