Darwin Nunez's stunning strike off the bench saw Liverpool through to the Carabao Cup quarter-finals to face West Ham after a 2-1 win at Bournemouth.
The Reds took a first-half lead through Cody Gakpo's close-range strike, after Harvey Elliott's 20-yard effort was spilled by Ionut Radu.
The Cherries named a near full-strength side, with only three changes from Saturday's win over Burnley, but were not at their best until after the break, when they deservedly levelled through Justin Kluivert's header from a corner.
- How the teams lined up | Match stats
- Carabao Cup fixtures | Results
- Stream the Carabao Cup and more with NOW
- Get Sky Sports | Download the Sky Sports app
But they would only be level for six minutes, before Nunez cut in from the left and lifted a sumptuous effort over Radu and in for the winner.
How Liverpool edged their way into quarter-finals
Despite the biblical conditions at the Vitality Stadium, both sides made good use of the momentum from their weekend wins in a lively affair on the south coast.
Bournemouth showed their hand first, with Kluivert denied from a tight angle by Caoimhin Kelleher, who was grateful to see the rebound cleared before the hosts could profit.
Harvey Elliott tested Radu from distance in a warning shot the Cherries did not heed, because from his next effort they would find the opener. The Romanian stopper could not hold his squirming drive, and instead Gakpo fired home from close-range.
Bournemouth emerged from the break re-energised and twice went close to forcing an equaliser before finally finding a way through. There was another threat ignored, this time from the home side, when Scott's corner was cleared off the Liverpool line by Joe Gomez.
From the ex-Bristol City midfielder's next delivery, they would not be so lucky, as Kluivert got his head to the ball to force it home from a couple of yards out.
The hosts' joy was short-lived. Nunez, only on from the bench for eight minutes, was held up by Smith on the right - but there was little the veteran defender could do about his sensational strike from wide.
Bournemouth pushed for a second equaliser and nearly found it from another Scott corner, but Liverpool held on to avenge last season's fourth-round exit at Manchester City to reach the quarter-finals this time around.
Klopp: Top game in tough conditions
Liverpool manager Jurgen Klopp:
"It was a top, top, top cup game. It's all about winning and getting through - and the good thing is I don't have to speak about the circumstances because everyone and saw it and felt it.
"We could've scored more goals in the first half, and in the second we realised it would've been a good idea because the wind changed the game again.
"We scored our second goal, a wonderful goal, and then fought extremely hard, had good moments, but it's all about attitudes in these moments.
"I saw how hard we really wanted it, and I'm really happy about it. It was a top cup game, in strange circumstances."
Iraola: It looked like we would score winner
Bournemouth manager Andoni Iraola:
"We had the advantage of the wind in the second half. We were struggling in the first half, it was really difficult with the wind.
"We couldn't kick it long and both teams were struggling to build up. At that moment we were putting on a lot of pressure and it looked like we could have scored a second one and win the game.
"But at the end they made the difference with Darwin's goal. I think it was an amazing strike and probably when they were in their worst moment of the game, it gave them the winning goal."
What's next?
Bournemouth head to champions Manchester City in the Premier League on Saturday; kick-off 3pm.
Liverpool head to Kenilworth Road on Sunday as they face Luton in the league, live on Sky Sports from 4pm; kick-off 4.30pm.