Paisley saw his team clinch the league title narrowly ahead of contenders Queens Park Rangers.
In a climax to the season, Liverpool needed to either win or secure a low-scoring draw against relegation-threatened Wolverhampton Wanderers.
With 14 minutes left for play and despite constant pressure in the second half, the Reds trailed to a Steve Kindon strike for Wolves.
The title was slipping away from Liverpool but three late goals from Kevin Keegan, John Toshack and Ray Kennedy in front of away support ensured Liverpool's ninth title and Bob Paisley's first trophy.
In the UEFA Cup, Liverpool overcame Barcelona in the semi-finals, to set up a final with Club Brugge.