Arne Slot's men extended their gaping lead over second-placed Arsenal, who have a game in hand, but lost further ground after being held to a 0-0 draw by Nottingham Forest. Newcastle slipped one spot to sixth, three points behind fourth-placed Manchester City.
Szoboszlai struck in the 11th minute at a rain-drenched Anfield when Luis Diaz worked the ball down the left before cutting it back for the unmarked Hungarian, whom Newcastle's Sandro Tonali had allowed to dart away into space.
The midfielder fired home a close-range shot that sailed through two sets of legs and past goalkeeper Nick Pope, the first time he has scored in back-to-back games for Liverpool.
Newcastle were better after the break, but Mac Allister doubled the home side's lead in the 63rd minute, when Mohamed Salah cut the ball back for the Argentinian, who punished the visitors for their sloppy defending with a blistering shot into the top corner.
"It is the desire, the desire to win trophies," Mac Allister told TNT Sports about his team's consistency. "We know that this season we have maybe the opportunity to win some, so we are really happy working really hard, and hopefully we can keep on going."
The Anfield faithful celebrated Mac Allister's goal by breaking into a chorus of "We're going to win the league," while the television camera panned to Slot, forced to sit in the stands due to a touchline ban, jubilantly pumping his fists.
The manager served the first of a two-game suspension on Wednesday for a red card he was shown after the final whistle of the chaotic recent Merseyside derby and his assistant John Heitinga was in the dugout in Slot's place.
Eddie Howe's team suffered a huge blow before the game with Alexander Isak, who has scored 21 goals this season across all competitions, ruled out with a groin injury.
Callum Wilson was the Magpies' biggest threat, and spurned a terrific chance in the first half when he got behind Liverpool's defence. He took a couple of touches before chipping the ball just wide, with his finishing rusty after playing just seven league games this season due to injuries.
Liverpool, who had 12 shots to Newcastle's three, had several late chances to add to their lead with talisman Salah front and centre.
He sprinted down the right before sending a beautiful pass to the far post for Diaz, who stretched but poked the ball just wide.
Pope dived to push a Salah shot wide towards the end of normal time.
Ibrahima Konate briefly celebrated when he outjumped Pope to head the ball home, but the Liverpool defender was adjudged to have fouled the keeper.
Cody Gakpo had a chance with a dramatic overhead kick in added time, but sent the ball just wide of the net.
The Kop were in full voice as Liverpool cruised to their 32nd victory in 43 games across all competitions, the most victories in Europe's top five leagues and two wins better than Real Madrid.
Howe said it was not a "bad performance in any way" from his side.
"But with the two goals we could have done much better," he added. "Both were passes into our box that we did not get tight enough to their midfielders which is frustrating really."
Forest hold Arsenal to dim Gunners' title hopes
Arsenal’s faint title hopes dimmed even further after they were held to a 0-0 draw by Nottingham Forest despite dominating this morning's Premier League match at the City Ground between the second and third-placed teams in the table.
Arsenal were 11 points behind runaway leaders Liverpool, albeit with a game in hand, but failure to win extended the gap to 13 points after Liverpool later beat Newcastle United 2-0.
Forest remained six points behind Arsenal in third place, keeping up their hopes of Champions League football next season, as they advanced to 48 points.
They did well to absorb Arsenal’s pressure in the first half, restricting them to no shots on target, although the Gunners were inches away from opening the scoring in the 24th minute after left back Riccardo Calafiori struck the post with a shot.
Calafiori had been booked in the second minute and came close to giving away a penalty, when he appeared to impede Callum Hudson-Odoi’s progress into the Arsenal box.
It was no surprise that he did not come back out after the break as Arsenal manager Mikel Arteta preferred not to risk going down to 10 men if Calafiori was booked again.
A dip of the shoulder from Ethan Nwaneri near the end of the first half set up a chance at the near post but it was blocked before the Arsenal attacker could get his effort away.
Makeshift forward Mikel Merino’s 53rd-minute header from Declan Rice's corner was the visitors’ first effort on target but it was parried by Forest keeper Matz Sels.
Arsenal were full of innovation with their set-piece routines, Calafiori's replacement Kieran Tierney heading narrowly wide from another corner.
Forest took 64 minutes to win their first corner and five minutes later their top scorer Chris Wood forced a routine save out of David Raya in the Arsenal goal.
It was a second successive match without a goal for Arsenal after they lost at home to West Ham United and Forest have won only one of their last five league games.
"We dominated the game. We tried in many different ways. We insisted but lacked that spark, that final pass to unlock a well organised team. We have to generate more shots on target," Arteta said.
