Lewis Koumas had given the young Reds an early advantage in the clash but Harrison Jones was quickly on target to equalise.
Both teams carved out chances across the 90 minutes and the hosts, in addition to hitting the woodwork twice, got the winner through Timur Tuterov.
Bajcetic started and – as pre-planned – completed a half for Barry Lewtas’ side as he continues his comeback from injury.
Liverpool’s bright start at the Eppleton Colliery Welfare Ground was punctuated by an opening goal in the eighth minute.
Koumas’ dogged high press saw him take the ball off Henry Fieldson on the edge of the Sunderland box, and he moved forward to swipe a reverse finish inside the left post.
The hosts’ response to the concession was impressive and the Reds needed Fabian Mrozek to race off his line and produce a sprawling block to deny Caden Kelly when he was found free in the area.
Pressure continued from Sunderland and it translated into an equaliser with 18 on the clock.
A corner kick from the left was partially punched away by Mrozek, but it came to Jones, who sent a first-time shot straight back into the Liverpool net.
Midway through the half, James McConnell almost produced a wonder goal against his former club. The midfielder drove past three opponents to bound into the box, but his strike was lifted over the bar.
Sunderland’s threat was persistent, though, and they were a whisker away from getting in front just before the 30-minute mark.
From an attack down the left-hand side, the ball was served into the centre for Tuterov, whose shot was kicked away by an outstretched Mrozek leg.
Trey Nyoni’s thump from 20 yards was tipped over at the other end, and later Koumas skipped in off the left wing and came close to emulating his earlier goal – but this time his hit bounced inches wide of the left post.
In the first exchanges of the second half, Jones sliced over from close range for Sunderland and Kaide Gordon stung the palms of the goalkeeper at the other end.
Nine minutes after the restart, the home team got ahead. The influential Tommy Watson scampered away along the left and drilled in a cross that was tucked home from yards out by Tuterov.
Liverpool had a couple of let-offs as the Black Cats pressed on, Tuterov nudging against the crossbar when Mrozek could not collect a deep free-kick and the Reds ’keeper deflecting a Watson effort onto the same part of the woodwork.
Mrozek was unbeatable at times, with a string of saves throughout the second half limiting the deficit to one – and drawing applause from the crowd.
His efforts almost paid off when substitute Harvey Blair sent Koumas through late on, but the forward was thwarted by a pivotal challenge that ensured Sunderland collected all three points.
TEAM
Liverpool U21s: Mrozek, Williams, Pinnington (Davidson, 63), McConnell (Pilling, 70), Nallo, Bajcetic (Miles, 46), Gordon, Nyoni, Danns (Blair, 74), Clark, Koumas.
Unused sub: Poytress.
NEXT UP
The young Reds’ final match of the regulation league campaign before the play-offs sees Arsenal visit the Kirkby Academy.
Kick-off on Sunday (April 28) is 1pm BST.
