The first-team striker was part of a strong line-up at St George’s Park which also featured Nathaniel Clyne – returning after a long-term back injury – and Joe Gomez in defence.
And Solanke was the difference between the sides, knocking home two excellent finishes before the break – and a simpler one in the second half – to earn a victory that was complemented by Bobby Adekanye’s late strike and sends Neil Critchley’s team into the competition’s knockout stage.
The 20-year-old’s first sight of goal was on eight minutes but he could not fully control Herbie Kane’s cross into the middle under growing pressure.
Oliver Shenton threatened Liverpool shortly after the quarter-hour but as he shaped to let fly from the edge of the area the midfielder was blocked out.
Within moments, Yan Dhanda broke clear at the other end – bursting forward from Solanke’s pass – and saw his fierce blast towards the near post punched out by Daniel Gyollai.
But the Stoke goalkeeper could do nothing to stop two goals ahead of the interval.
On 25 minutes, Elijah Dixon-Bonner fed Kane and the subsequent forward pass released Solanke for a calm finish rolled across the ‘keeper into the bottom corner.
And the England youth international was even more clinical with 40 on the clock. Curtis Jones’ reverse pass opened up space in the left channel to crack an unstoppable hit inside the far post.
Liverpool kept Stoke at arm’s length for much of the second half and, precisely midway through it, made sure there was no chance of a comeback.
Again it was Jones with the assist, squaring from the right flank for Solanke to tap into an unguarded net after a Potters defender’s touch landed perfectly for the No.9.
There was still time for an outstanding 84th-minute effort from substitute Adekanye, who dribbled off the right flank and past two challenges before thumping a shot into the left corner from 20 yards.
Kane received a late red card but Critchley’s side nevertheless safely booked their place in the last 16 and moved to the summit of Group G, though Bristol City can reclaim top spot with their game in hand.
Liverpool U23s: Grabara, Clyne, Gallacher, Gomez, Johnston, Dixon-Bonner (Lewis, 56), Camacho (Adekanye, 68), Kane, Solanke, Jones, Dhanda.
Unused substitutes: Kelleher, Masterson, Gomes.