Liverpool - in their third friendly of the summer compared to Palace's first - were the team on top and went close a few times in the first-half, though could not convert their opportunities.
But it was summer signing and substitute Solanke with the breakthrough when the teenager finished a fine team move by burying a powerful 20-yard strike into the far bottom corner on the hour mark.
The Reds made it 2-0 on 79 minutes after Philippe Coutinho drove forward and looked to James Milner on the left. His low cross into the penalty area was blocked by Martin Kelly, the Brazilian's attempt, it fell to Divock Origi to make it 2-0 from close-range.
The Reds' victory means they face Leicester in the final after the Foxes beat West Bromwich Albion on penalties earlier in the afternoon.
Palace will face the Baggies in a third-placed play-off, with both games on Saturday and played at the same venue, the Hong Kong Stadium.
Klopp and de Boer field strong line-ups
Trent Alexander-Arnold started at right-back with Nathaniel Clyne out injured, while club-record summer signing Mohamed Salah made just his second Liverpool pre-season appearance and 17-year-old Ben Woodburn started in central midfield.
Palace handed young forward Keshi Anderson a chance to impress out wide as Frank de Boer fielded a near full-strength starting line-up including Wilfried Zaha while utilising a back-three formation.
Zaha and Salah the first-half stand-outs
In a first-half high on intensity but short on quality, Liverpool pressed high with typical energy early on while Zaha - a consistent thorn in the Reds' side whenever the two teams meet - proved Palace's chief threat with his twists and turns on the ball.
Liverpool almost made it 1-0 on 12 minutes after Woodburn and Alexander-Arnold combined on the right but Daniel Sturridge's effort from a low cross was deflected just wide by Scott Dann.
The Reds went close again when Henderson clipped a ball deep into the box where Sturridge laid on a cute back-heel for Lallana, though the midfielder fired a first-time shot off target from 12 yards.
Salah - one of Liverpool's brightest players in the opening 45 minutes - almost curled a trademark left-footer into the far top corner after a run across the edge of the box, but fired just over.
Simon Mignolet was called upon to make his first save before the half-hour mark, closing down the space to deny Anderson's attempt after the attacker's one-two with Andros Townsend.
The conditions, the overbearing humidity and badly torn-up pitch, affected proceedings but Liverpool always looked the likelier of scoring first.
Sturridge forced another save after cutting inside and firing a low right-footed shot from distance which Wayne Hennessey could only palm out into the box.
Substitute Solanke puts Reds in front with first Liverpool goal
With the competition's rules stating that only four changes could be made at any one time, Liverpool changed their entire back-four at half-time, with another six changes all coming before the 50th minute.
Palace, meanwhile, kept the eleven that started the evening. Coutinho almost made an instant contribution, but curled over the bar after coming inside from the left in trademark fashion.
But the game's long-awaited opening goal finally came on the hour mark as Solanke scored for the first time since joining Liverpool from Chelsea.
Excellent build-up saw Divock Origi flick Coutinho's pass into Solanke's path on the edge of the area and the striker spun goalwards, took a touch and fired a right-footed effort across the goalkeeper and into the far corner.
Grujić lucky not to see red before Origi makes it two
Marko Grujić - guilty of a poor challenge when Liverpool played Palace in the Premier League back in May - was fortunate not to be sent off after a nasty tackle on Zaha which understandably enraged the winger, before the Serbian drove a 30-yard effort just past the post.
And Liverpool doubled their advantage with 10 minutes to play. Milner found Coutinho driving into the middle of the box but though the playmaker's effort was blocked, Origi was on hand to slam home the loose ball.
Ryan Kent, linked with a season-long loan move to Hull City, almost forced a third with a long-range effort that forced Hennessey to push wide, before Grujić saw an effort stabbed clear and Coutinho failed to test the Palace 'keeper with an underwhelming shot after a sublime solo dribble.
But Liverpool saw out victory and will face Leicester in three days' time, leaving Palace to contest a third-placed play-off against West Brom.