Bukayo Saka showed persistence to fire past Jose Sa after six minutes, before Martin Odegaard coolly completed a fine team move from the edge of the area seven minutes later.
Al Nassr managed the game expertly and condemned Gallardo's side to a third consecutive Saudi Pro League defeat as the visitors close the gap at the top of the table to seven points over runaway leaders Al Hilal.
Abraham slotted past Marc-Andre ter Stegen to hand the Blues the lead seven minutes before the interval, and Barkley rounded off an encouraging team performance with an effort from 20 yards nine minutes from time.
City were seven points behind Liverpool on January 19 but Wednesday's win sees them move level with Jurgen Klopp's Reds, the defending champions taking over at the summit on goal difference.
Memphis Depay's close-range finish put United in front in the 37th minute, but Pione Sisto -- capitalising on a Michael Carrick error -- equalised seven minutes later, and a fine strike from Midtjylland substitute Paul Onuachu with 13 minutes
The Gunners have won seven games in a row in all competitions - scoring 23 goals - and are undefeated in 11 matches. Their last defeat was at home to Liverpool on the opening day of the Premier League season.
Manchester United put in a dominant performance to beat a terrible Crystal Palace, who have lost all seven Premier League games this season without scoring.
Jurgen Klopp's side have won their past seven games to bolster their push for a top-four finish and now lie a point behind Newcastle and Manchester United, albeit having played a game more.
Kane, who scored his first Champions League goal for Bayern in the midweek win over Manchester United, has now scored seven times in just five Bundesliga appearances.
Diego Costa's smart finish put Chelsea level on the night before half-time, but his departure through injury on the hour and Ibrahimovic's simple finish from Angel di Maria's delivery seven minutes later sent PSG into the last eight.
The Spaniard, Eden Hazard and Gary Cahill - all back in the starting XI - got the goals that extended the Blues' advantage over second-placed Tottenham to seven points.
The Blues' second-round victory over fourth-tier AFC Wimbledon was one of just two from seven matches across all competitions so far this season amid a torrid start to life back in English football for manager Mauricio Pochettino, who makes
Aaron Ramsey's instinctive flick gave Arsenal the lead just before the interval - but the game looked to have turned in the space of seven minutes before the hour.
Messi's one weakness was also exposed as he failed to find the net from the penalty spot seven minutes before half-time. However, he settled the visitors' nerves by drilling home with the aid of a deflection just after the break.
The Belgian winger opened the scoring with a stunning curled finish from the edge of the box, before laying on goals for Bernardo Silva and Manuel Akanji as the champions hit three goals in seven first-half minutes.
The home side ought to have taken the lead on seven minutes when Gautier Lloris, in front of goal with the keeper out of commission, placed his finish straight at Carlos Soler, covering on the line.