Welsh winger Harry Wilson was the star of the show at Anfield as Liverpool won their sixth game out of six to stay top of Premier League 2, the under-23 equivalent of the Premier League.
It was Wilson – so often the Red’s key man – who put his side in front, after only 29 seconds.
A cross from the left found him in the penalty area, and his headed effort looped over the goalkeeper and into the back of the net.
For the opening stages, it was all Liverpool pressure: before five minutes had elapsed, Rhian Brewster got in behind and attempted to make it 2-0, but was unable to get a strong enough touch.
After eight minutes, Marko Grujic was loose in possession and gave away a free-kick on the edge of the area when he cynically tugged back his opponent, but the resulting kick was central, with goalkeeper Kelleher able to gather easily a let-off for the Serb who had been far too relaxed on the ball.
Lazar Markovic, his fellow countryman, appearing at Anfield on a rare occasion, played a great through-ball across the pitch to Ben Woodburn, but he could only drag his shot wide of the target.
That pass, and an assist later on, were probably the highlights of another difficult night for the £20 million man, as he had little impact from there on in.
Brewster was again through before the quarter hour mark, but when his first effort was rebounded off the goalkeeper back to him, he could only slice wide under pressure.
Tottenham’s biggest threats came when Liverpool dallied in possession. On one such occasion, Kelleher took a long time to clear the ball when being closed down, and he was fortunate to clear in the nick of time.
Just a minute after that scare, Wilson grabbed his second of the evening, sweeping into the corner with his right foot after being teed up by Markovic.
Loose play when building up from the back led to a Tottenham shot, but Kelleher gathered simply.
Spurs were struggling to create chances themselves, and Kelleher’s only tests were coming as a result of slack passing on his teammate’s behalf.
It was a penalty that gave Tottenham a lifeline, dispatched by Marcus Edwards on 20 minutes. The spot kick had been awarded for a minimal foul, leaving the assembled crowd on the Kop unimpressed, but the penalty kick itself was perfectly placed.
Having had a nervy beginning to the game, Spurs found some confidence from the goal out of the blue, as they began to settle down.
A poor kick out from Kelleher gave them even more encouragement, but his defence eventually mopped up the danger, before Brewster went up the other end and used his pace to create a chance for Wilson, whose effort went over the bar.
Ben Woodburn was involved in a scuffle after half an hour when he appeared to be kicked as he lay on the floor, with the referee booking Brewster for his involvement in the aftermath.
The flare-up, and the lengthy delay as the referee gained back control, knocked Liverpool out of their stride and seemed to galvanise the visitors, and they equalised soon later.
Christian Maghoma curled a shot into the top corner with his right foot, and from 2-0 down and looking well off the pace, Tottenham were somehow level.
Markovic, playing off the left-hand side, was too weak in possession and lost out easily, which led to a corner kick being given, but Kelleher punched clear competently.
Since equalising, Spurs had gotten on top, and Kelleher was again called into action a couple of times as they pressed for a goal to put them ahead.
It was Liverpool, though, who went in a goal in front at the break, when Wilson completed his hat-trick with a left-footed curler from the right-hand corner of the box.
His link-up with Woodburn opened up the space, and from then on there was no doubt that the ball would end up in the back of the net. That goal was against the run of play, but the half as a whole had warranted a Liverpool lead.
After play restarted for the second half, Markovic found himself in behind but could not produce a final pass with Brewster free in the centre, but it was not long until the striker was found.
Grujic played a long pass over the top of the defence, and the 17-year-old clinically lifted a deft chip over the onrushing goalkeeper to restore Liverpool’s two-goal advantage.
The knee-slide in front of the Kop showed what it meant to the youngster to notch at Anfield, and the goal came at a crucial time.
Grujic could have scored himself immediately afterwards, but blasted a shot well over the top after more good work from Wilson on the right.
Woodburn also shot over when set up by Ovie Ejaria, after the midfielder had shown great feet to beat three men on the left side of the pitch.
Markovic was replaced after 63 minutes, with Cameron Brannagan coming on in his place. The winger had done nothing to suggest a first-team return might be on the horizon, and apart from one or two passes had only been sporadically involved.
With more than three quarters of the game gone, Wilson nearly notched a fourth goal when the Spurs goalkeeper’s headed clearance fell for him. From thirty five or more yards out, he attempted a chip with the keeper of his line, but the ball sailed just over the crossbar.
Yan Dhanda, who scored a memorable winner a couple of weeks ago in the 1-0 win over Manchester City, replaced Woodburn for the final ten minutes, but by now Tottenham had seemingly given up on an unlikely comeback.
Liverpool managed the game professionally, unwilling to let a two-goal cushion slip for the second time in the match, and the final stages were completed without alarm.
When Wilson and Dhanda combined on the breakaway, a cynical foul led to a free-kick, which the substitute took himself, but the goalkeeper held the shot.
Brewster also had a chance to double his tally, but he could only deflect Ejaria’s cross over the bar from inside the six-yard box.
Liverpool probably should have had a penalty when a foul was given just outside the area when it looked like the contact was inside the box, but the free-kick came to nothing.
Liverpool deservedly won the game and remain top of Premier League 2 after six games. They will face Charlton next in a game next Friday night.