A tense contest saw little by way of clear cut chances, but the Reds' second-string turned in a battling display against a Blues side that contained several first-team fringe players.
And it was one of those, Baxter, who fired home a volley in the 90th minute to harshly condemn Liverpool to a fourth successive defeat.
The result means Liverpool's outside hopes of being crowned Barclays Premier Reserve League North champions are over, but John McMahon will no doubt be pleased by the character shown by his men after suffering three back-to-back losses which derailed their title charge.
Ahead of the game, the second-string boss acknowledged his side's hopes of lifting the Championship had been all-but ended by the disappointing Friday night defeat in Burnley.
That loss at Turf Moore had been described by McMahon as one of his team's worst performances of the season - and the gaffer demanded a response from his troops against their Everton counterparts, particularly as it was still mathematically possible for his charges to end the term with the trophy.
His team selection included several promising youngsters such as 17-year-old Czech defender Jakub Sokolik, John Flanagan, Nicolaj Kohlert and Lauri Dalla Valle.
The Blues, meanwhile, selected a powerful starting XI that included the likes of Philippe Senderos, Victor Anichebe and Baxter.
The opening exchanges were typically frenetic and Gerardo Bruna fired an early warning shot, curling wide of Ian Turner's far post from a difficult angle inside the opening two minutes, while at the other end, Baxter drilled over from distance.
However, chances were proving scarce for both sides in a gritty first-half contest, with neither able to enjoy a sustained period of possession.
It was David Martin who was forced to pull off the first save of the evening when the Liverpool goalkeeper got down well to palm Baxter's stinging low free-kick around the base of the post on 27 minutes.
The Blues went closer still moments later as Victor Palsson's misplaced pass allowed Nathan Craig to send Anichebe bearing down on goal. The striker's low shot beat Martin, but lacked power allowing Palsson to make amends by clearing the danger from inside the six-yard box.
Everton quickly regained possession and Craig swung in a cross from the left, which was met by a downward header by James Wallace, but Martin was able to gather.
The Blues were beginning to build up a head of steam and Anichebe steered an effort narrowly wide after plucking Senderos' cross out of the air on 38 minutes to ensure the game remained scoreless at half-time.
Liverpool should have broken the deadlock six minutes after the restart as Nicolaj Kohlert's flick played Bruna into space in the left channel of the box, but the former Real Madrid starlet's low drive was repelled by the legs of Turner.
Back came the Blues and only a fine challenge by Palsson prevented Anichebe from getting a clear strike on goal. With Martin out of position having attempted to close down the forward, Craig delivered a cross back into the area, which was nodded wide of the open goal by Baxter.
There was suddenly a much more open feel to proceedings and Bruna cannoned a volley against the legs of Senderos when well positioned as the Reds took their turn to attack.
Amoo then powered past Luke Garbutt on two occasions, but both times his low cross to the near post intended for Dalla Valle was cleared by Everton defenders.
Liverpool were in the ascendancy and after Bruna's jinking run had fashioned a shooting chance for Kacaniklic, whose effort was blocked, Amoo drilled into the side netting.
Amoo's influence was growing and his powerful surge from the halfway line resulted in the youngster hammering a strike narrowly over the bar on 68 minutes.
With eight minutes remaining, the livewire winger caused havoc in the Everton defence once more, and his low centre found Kohlert in space, but the strike was blocked brilliantly by the diving Turner.
As time ebbed away, Bruna clipped a free-kick over the right edge of the box as the home side pressed in search of a winner, but it was Everton who won it in stoppage-time when Baxter's stinging volley struck the underside of the crossbar and bounced over the line to leave the young Reds heartbroken.
Liverpoolfc.tv man of the match: David Amoo - The winger's powerful bursts forward created the Reds' best openings in the second half.
Liverpool Reserves: David Martin, John Flanagan, Alex Cooper, Jakub Sokolik, Victor Palsson, Steven Irwin, Gerardo Bruna, David Amoo, Lauri Dalla Valle, Nicolaj Kohlert, Alex Kacaniklic.
Subs: Conor Coady, Chris Oldfield, Jordy Brouwer, Thomas Ince, Jack Robinson.
Everton Reserves: Ian Turner, Aristote Nsiala, Luke Garbutt, James Wallace, Philippe Senderos, Shane Duffy, Nathan Craig (Shrodran Mustafi 65) , Hope Akpan, Victor Anichebe (Anton Peterlin 62), Jose Baxter, Adam Forshaw (Conor McAleny 46).