The meeting was held in Sheffield and ended with the score 1: 0 in favor of the hosts.
The only goal in the 30th minute was scored by Lee Mousse.
Sheffield scored 12 points and climbed to ninth place in the league table of the championship of England. Arsenal is on the fifth line with 15 points.
In the next round, Arsenal will play with Crystal Palace, and Sheffield with West Ham.
Earlier, Manchester United and Liverpool tied in the Premier League.