On 8 September 1888, Aston Villa's Gershom Cox (pictured in back, third from the right) scored the Football League's first goal when he found the net in the 30th minute of Villa's opening-day match against Wolverhampton Wanderers. Unfortunately for Cox and Villa, however, the net was his own.
On the same day, Preston North End captain Fred Dewhurst scored in the 3rd minute against Burnley (a match Preston went on to win 5-2). Athough records from that time are sparse, it is believed that Villa-Wolves kicked off at 3:00 p.m., while the Preston-Burnley match started at 3:50 p.m. So Cox's goal came at 3:30 and Dewhurst's goal came at 3:52.
Fortunately for Cox, his own goal was not the game-winner for Wolves, as Villa's Tom Green scored an equalizer to end the match at 1-1.
[2013 update: The BBC reported in July 2013 that, due to new research uncovered about the start times of the matches on that day, the first goal was scored by Bolton winger Kenny Davenport, who struck after just two minutes against Derby County.]