The Reds had endured a tough week with a 5-0 loss at the hands of Arsenal followed by the resignation of manager Neil Redfearn.
But Liverpool, under caretaker Chris Kirkland, responded at New Ferens Park by fighting back from 3-1 to draw 3-3 and clinch a bonus point with a 5-4 win on spot-kicks.
The contest got off to a breathless start with two goals inside the first three minutes.
Sophie Bradley-Auckland gave Liverpool a second-minute lead from Christie Murray’s left-wing corner, the linesman judging that Durham keeper Megan Borthwick had collected the defender’s shot behind the goal-line.
Durham’s response was instant, with Sarah Robson sliding in Emily Roberts, who slipped a shot under Anke Preuss.
And the Wildcats went ahead in the 21st minute when Roberts finished cleverly from Abi Cottam’s delivery.
Durham stretched their lead in the 57th minute.
The Reds failed to deal with another dangerous cross, this time Cottam heading powerfully beyond Preuss from Kathryn Hill’s ball from the left.
Liverpool pulled one back in the 70th minute when a diving Borthwick could not keep out Rinsola Babajide’s stunning left-foot strike from the edge of the box.
Substitute Yana Daniels spurned a chance for the Reds with her first touch but her fellow sub Courtney Sweetman-Kirk converted at the far post five minutes from time from Charles’s cross.
Preuss denied Roberts a hat-trick at the end of normal time to force penalties and saved from the two-goal Wildcats star in sudden-death, with Bradley-Auckland dispatching the winner.
Goal of the match
Rinsola Babajide opened her account for the season in some style with Liverpool’s second goal of the match 20 minutes from time.
Having been fed by Niamh Charles, the 20-year-old forward rifled home a sublime left-footed effort that was nigh-on unstoppable.
What they said
Liverpool’s Sophie Bradley-Auckland, who notched in normal time and also scored the decisive penalty kick, said: “That’s the most confident I’ve ever felt taking a penalty.
“I looked down the line on halfway and said: ‘who’s next?’ and everyone looked at me, so off I went.
“Hats off to Anke for some brilliant saves, when it went to penalties I wouldn’t have wanted anyone else in goal, she does that day-in, day out at training.
“We could have been down and out but the fight we’ve got in us showed on the pitch today.
“I always knew we were going to do it. We’d had a tough week and there were probably a few emotions before the game but once we got going, we found our feet and played the better football.
“Credit to Durham. They were very clinical in front of goal. Everything they hit seemed to go in the back of the net but we re-grouped and said: ‘we can do it’.”
Durham’s two-goal Emily Roberts said: “The girls put in a lot of hard graft. It was a very good game from us. It was just a shame we couldn’t quite finish it off at the end.
“Liverpool was always going to be a hard game but we scored three good goals from open play, which we are very happy with.
“We’ll take that forward into our Championship games.
“We’re not very good at penalties, especially me – I don’t like taking penalties and I apologised to the girls for missing one.
“I nearly scored at the end (of normal time). It was an alright shot and I think it moved a bit in the air. It was unlucky but it was a cracking save by Anke.
“Overall, we are pleased. We’ve drawn against a Women’s Super League side and we can take that into our league games.”
Liverpool return to FA Women’s Super League action with a trip to Brighton & Hove Albion next time out.
Bradley-Auckland said: “We’ve got a lot of work to do. That (at Durham) was still not our best performance. There are so many things we can do better, especially defensively.
“That’s the great thing about this team. Yes, we’ve won on penalties, but we now we have so much more we can give.
“It’s great to be back on the training field. We turn up and play football because we love it.
“We don’t do it for money or fame. We do it because we’ve loved playing football since we were little girls. Whatever is thrown at us, we’ll keep going.
“It’s going to be a long journey but it will be a good game. Brighton are a good side. I played against them last year when I played for Doncaster.
“Brighton are a good team. It will take a lot for us to beat them but I’m confident we can do it.”
Durham, meanwhile, are in action at New Ferens Park again in the FA Women’s Championship, with Charlton Athletic the visitors.
“It’s our first home game in the Championship and we’re looking forward to it,” said Roberts.
“We’ve not seen a lot of Charlton. Obviously, they are new to the league, so we’ll have to be wary about what they are going to bring but if we play like we did against Liverpool, then it should be a good game.
“The performance and result against Liverpool should be good for our confidence – definitely.
“I think we have a good, solid team, who are working hard for each other, and you can see it coming together on the pitch.
“It was a great season last year and it would be great to go one better. That’s the aim, anyway.”
Roberts 3, 21, Cottam 57
Bradley-Auckland 2, Babajide 70, Sweetman-Kirk 86
Liverpool won 5-4 on penalties
Durham (4-4-2): Megan Borthwick, Abby Holmes, Sarah Robson, Becky Salicki, Kathryn Hill; Abi Cottam, Sarah Robson, Rachel Lee, Emily Roberts, Beth Hepple, Zoe Ness
Substitutes: Nicki Gears for Lee 55, Ellie Christon for Salicki 67
Substitutes not used: Hannah Reid, Chloe Knott
Goals: Roberts 3, 21, Cottam 57
Liverpool (4-1-4-1): Anke Preuss, Satara Murray, Sophie Bradley-Auckland, Jasmine Matthews, Leighanne Robe; Laura Coombs; Rinsola Babajide, Amy Rodgers, Christie Murray, Niamh Charles, Jess Clarke
Substitutes: Kirsty Linnett for Clarke 61, Courtney Sweetman-Kirk for Babajide 75, Yana Daniels for Rodgers 82
Substitutes not used: Fran Kitching, Missy-Bo Kearns
Goals: Bradley-Auckland 2, Babajide 70, Sweetman-Kirk 86
Referee: Lucy Oliver
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