Darwin Nunez struck a 99th minute winner as the reds maintained position at the top of the Premier League at Nottingham's City Ground.
He glided in a deft back post header to send the travelling fans home jubilant.
The reds continued with an under-strength starting XI, although they did eventually welcome back Szoboszlai, Endo and Nunez in the second half from the bench.
It was the reds fourth win in a punishing 10 days that has seen them collect the League Cup, advance in the FA Cup and stick six more points on their Premier League title push.
It was Liverpool's first victory at the City Ground in almost 40 years (since 1984) and the goal came at the end of an extended period of extra time brought about by some Forest time-wasting as they came under increasing red pressure at the end of the second half.
Kelleher was once again in top form, and Divock Origi (playing for Forest) had threaded a ball through to Elanga in the first half that Kelleher impressively kept out.
In his recent spell in the side, Liverpool's xG for conceding is just over 5 goals. He hasn't conceded any.
Clearly upset about another last minute defeat, the home side sent out their new employee Mark Clattenburg to complain about a decision from two minutes earlier in the move. A mistake that similarly had gone against Liverpool in the first half when a drop ball had been returned to the keeper.
The reds deserved the win though and Klopp was delighted to get the points that their pressure had deserved.
Attention now turns to the Europa League before a crunch clash against Manchester City at Anfield.
VIDEO HIGHLIGHTS: Nottingham Forest 0-1 Liverpool
