Daniel Sturridge scored his first goals in six months as Liverpool held on to win 3-2 and ease the pressure on Brendan Rodgers after an entertaining encounter with Aston Villa at Anfield.
Sturridge, making his second appearance after hip surgery, found the net twice in the second half after James Milner had given the home side the lead in the second minute.
But a brace from Rudy Gestede meant Villa were right in the game throughout and ensured a tense finale for the home manager and supporters alike.
Liverpool had got off to the perfect start as Milner gave them the lead after 66 seconds, collecting a pass from Coutinho on the edge of the box with one touch and finding the bottom corner with his second to lift the tension at Anfield.
The hosts remained on top for much of the first half with Coutinho pulling the strings in midfield and Alberto Moreno, in particular, a threat down the left.
Danny Ings also looked sharp after two goals in his previous two games and tested Guzan with a shot from just outside the box before curling another over the bar moments later.
However, Villa should have been level after a counter-attack ended with Alan Hutton's cross only being cleared to Rudy Gestede by Emre Can. The striker took the shot first time but sliced it wide from just inside the box.
The pattern of play returned to the norm with Liverpool pushing forward without creating any further chances of note and the visitors struggling to get out of their half before Villa went close again from another break.
It was Hutton down the right who again provided the cross after Mamadou Sakho had tackled Jack Grealish. Simon Mignolet punched it half clear but Ashley Westwood was on the edge of the box and it took a block from Martin Skrtel to deny him an equaliser.
That was how it stayed until the break and it seemed as if little had changed once play restarted. The home side stayed on the front foot with Villa happy to sit deep and counter when possible.
Nathaniel Clyne very nearly doubled Liverpool's lead soon after the interval after Milner's well-struck shot was parried into his path by Guzan. However, Jordan Amavi threw himself in front of the shot to prevent a certain goal.
Liverpool's were not to be denied though and they gave themselves a two-goal cushion just before the hour mark.
The ball came in to Milner on the edge of the box and he flicked it with the outside of his foot into the path of Sturridge who took the volley on first time, finding the far corner with unerring accuracy (59).
If that brought relief to the home fans, tension abounded again six minutes later when Gestede stabbed home unmarked from Hutton's cross.
Given their recent form, few would have been surprised had the hosts wilted at this point. Instead though, they pressed forward again to score their third less than a minute later.
Sturridge was again the goalscorer, picking up the ball on the left corner of the area and playing a one-two with Coutinho before rolling the ball into the bottom corner with his right foot.
It was the kind of calm, clinical finishing that Liverpool have so missed in his absence.
Tim Sherwood's men refused to accept they were beaten though and were back within a goal of their hosts just four minutes later.
Amavi put in a hanging cross from the left and Gestede attacked it before rising above Sakho to bullet an unstoppable header past Mignolet.
After four goals in 12 frenetic second-half minutes, Liverpool went about trying to take some time out of the game, slowing the tempo and gradually reasserting their authority on proceedings.
With Villa now adopting a more adventurous approach, the chances were there for Liverpool to add a fourth.
The best of these came after a quick passing move with Ings playing in Sturridge who was denied a hat-trick as his right foot shot was tipped round the post by Guzan.
Micah Richards headed just over from a free-kick at the other end while Coutinho and Ings had chances to seal the three points for Rodgers' side.
However, Liverpool survived what could have been a very edgy last few minutes relatively comfortably to hold on and take three much-needed points.
Live Ford Super Sunday
Charlie Nicholas's Soccer Saturday verdict
"It was the quickness of mind, of feet, from Daniel Sturridge but it was worth waiting for because he could've scored five today.
"To score in the first minute, over 60 seconds, is awful for Aston Villa but such a good pick-me-up for Liverpool. It was [James] Milner, picked in a nice spot, nice control, no pressure on him and drills it in. You thought, surely that would ease the tension?
"It started to ease off a little, but the crosses started coming in and you could see the panic in with the back three.
"Ings could've scored two, Sturridge could've scored five, Guzan had some very good saves and in the end it was three points which was extremely well earned and well needed. For Brendan Rodgers, this is a massive pick-me-up."
Liverpool: Mignolet (6), Can (7), Skrtel (6), Sakho (6), Clyne (7), Milner (7), Lucas (8), Moreno (7), Coutinho (7), Ings (6), Sturridge (8).
Subs: Allen (6).
Aston Villa: Guzan (7), Hutton (7), Richards (6), Lescott (6), Amavi (6), Sanchez (6), Westwood (6), Gueye (6), Grealish (4), Sinclair (5), Gestede (8).
Subs: Veretout (5), Traore (6).
Man of the match: Daniel Sturridge