It happened during the 1981 FA Cup semi-final between Tottenham Hotspur and Wolverhampton Wanderers.
Spurs fans spilled on to the track at the Leppings Lane end - the same area where the 1989 tragedy unfolded.
The jury saw a clip of game footage including fans climbing fences.
On that occasion 38 supporters suffered injuries including broken arms, a broken leg and stitches.
Profiles of all those who died
Det Supt Neil Malkin, the senior investigating officer for Operation Resolve - the police criminal investigation into the 1989 disaster - said it may have been linked to Tottenham scoring a goal which caused a crowd surge.
Mr Malkin is giving evidence to provide the jury with context in which the layout of the terrace was altered by the introduction of radial fencing.
The terraces were divided into three pens in the months following the 1981 match.
Christina Lambert QC, counsel for the inquests, said that immediately before the 1981 cup tie there was congestion at the Leppings Lane turnstiles.
Mr Malkin confirmed that Gate C at the turnstiles was opened to alleviate the congestion and a number of fans entered.
He said it was "likely" that the "focus of the crush" in 1981 was in "a rather different position" to the 1989 incident.
Two perimeter gates were opened to let fans out.
Between 100 and 250 fans were estimated to have moved out of the terrace following the 1981 crush, the jury was told.
Following the match, it emerged that the stipulated capacity may have been exceeded by 335.
Ninety-six fans died as a result of the crush at the 1989 FA Cup semi-final.
The inquests continue.
Thirty-eight fans were reportedly injured in a "crushing incident" at Hillsborough eight years before the tragedy which killed 96 people, their inquests have been told.