The Anfield fixture had initially been scheduled as the second leg, but last week's match was postponed due to a number of coronavirus cases within Liverpool's squad.
Arsenal was thrashed 4-0 in its previous trip to the ground in November but a depleted Gunners side ensured the second leg will start on level terms following a stoic display, which was complicated by Granit Xhaka's 24th-minute red card.
Missing Mohamed Salah and Sadio Mane due to the Africa Cup of Nations, Liverpool toiled in front of a packed Arsenal defence and when a golden chance did finally come, Minamino fluffed his lines.
Already shorn of the injured Emile Smith Rowe and Martin Odegaard, who had tested positive for COVID-19, Arsenal was dealt another blow when Cedric Soares limped off in the 11th minute.
The visitor would surely have been behind if not for Ben White's intervention, with the defender just managing to deny Roberto Firmino a tap-in.
Though it weathered an early storm, Arsenal's task was made harder when Xhaka received his marching orders for a desperate, high swipe at Diogo Jota just outside the Gunners' area.
Minamino, Liverpool's hero from the quarter-final win over Leicester City, almost caught out Aaron Ramsdale early in the second half with a long-range cross-shot that dropped just wide.
Alisson had to be alert to thwart Bukayo Saka at the other end in a rare Arsenal attack, but Minamino should have won it late on.
Ramsdale flapped at a cross and left his goal gaping, yet Minamino's first-time effort flew high over the crossbar.