Match reportVan Dijk and Szoboszlai score in Liverpool win away at Sheffield United
The Reds captain netted the opener in the Bramall Lane affair in the 37th minute with a fine finish from Trent Alexander-Arnold's corner.
Szoboszlai then wrapped up the win, which keeps Jürgen Klopp's men second in the top-flight standings, deep into second-half added time.
Team news
Klopp opted to make four changes to the side that defeated Fulham 4-3 in dramatic fashion at Anfield last weekend.
In came Joe Gomez and Ibrahima Konate to the backline, with Wataru Endo and Cody Gakpo also handed starts.
Kelleher, Alexander-Arnold, Konate, Van Dijk, Gomez, Endo, Mac Allister (Jones, 59), Szoboszlai, Diaz (Nunez, 67), Salah (Elliott, 67), Gakpo (Gravenberch, 86).
Unused subs: Adrian, Pitaluga, Tsimikas, Quansah, Bradley.
First half
After a relatively slow opening 10 minutes, both teams then created good opportunities to open the scoring.
Endo collected possession in a central area and sprayed an accurate pass to release Luis Diaz on the left, from where he floated an inviting cross into the box. It found Mohamed Salah but he ended up slicing a volley well over.
At the other end, Caoimhin Kelleher stuck out an arm to keep out James McAtee's finish after Cameron Archer pinched the ball off Gomez and drove at goal.
The Blades' next venture forwards, led by Archer, was stopped in the penalty area by the covering Van Dijk.
Liverpool then threatened with a trio of corners in quick succession, Konate forcing a good save from Wes Foderingham after the ball was worked back into the box.
They would make their next one count, however, when Van Dijk created space for himself in the area and thumped Alexander-Arnold's outswinging delivery past Foderingham to make it 1-0.
The skipper nearly grabbed a second a few minutes later but headed over another Alexander-Arnold corner, with Salah scuffing a shot straight at the goalkeeper with the Reds' last clear-cut opportunity of the half.
Second half
Liverpool remained threatening with their set-pieces and would have gone two goals up 11 minutes into the second period had it not been for a brilliant intervention from Foderingham.
Alexander-Arnold's corner, from the right, was met by Salah, who unleashed a ferocious first-time hit that was tipped over by United's stopper.
Foderingham ensured it remained 1-0 heading into the final 10 minutes when he came out on top in a one-on-one situation with substitute Darwin Nunez. Gomez then blazed over in the aftermath.
That gave the hosts encouragement as they applied a spell of pressure on the Reds' defence. But McAtee had a penalty appeal turned down and Archer didn't connect properly with his effort from inside the box.
As United pushed hard for the leveller, Nunez exploited the space left in behind by crossing to find the vacant Szoboszlai in front of goal, allowing him to convert and clinch the points.
Team newsConfirmed Liverpool line-up v Bayer Leverkusen
AcademyYouth League match report: Liverpool 4-1 Bayer Leverkusen
Programme notesArne Slot: The biggest respect we can pay Xabi is to be the best Liverpool
Programme notesVirgil van Dijk: We need to take Brighton positives into Leverkusen clash
Champions LeagueThe opposition lowdown: Bayer Leverkusen