Creating history can seldom have been this comfortable. Wigan recorded their first-ever win at Anfield without having to conjure anything ingenious: their diligence and determination, added to the deficiencies of their hosts, were enough. Even the visiting manager, Roberto Martinez, admitted his team had played better in each of their last six matches without winning, though that obviously did not deflate his delight at a result that will buoy their survival bid.

Having lost four of their five previous league matches, including Wednesday's alarming capitulation against another team in the relegation zone, Queens Park Rangers, Liverpool needed an authoritative victory to subdue minor rumblings of Anfield heresy: suggestions that Kenny Dalglish is not the managerial messiah the club crave despite the conquest of the Carling Cup. A settled formation is not something Dalglish appears to believe in and for this outing he decided that a 4-1-4-1 would be the best way of ensuring Luis Suárez, that paradoxically dangerous but goal-shy striker, got ample support up front.

The ploy worked almost too well in the fifth minute when Suárez and Jordan Henderson got in each other's way after Jay Spearing had served the first defence-splitting pass of the match. And that set the tone for the home team's display, as their disjointedness drew constant groans from the crowd.

By the 15th minute, the discontent was evident on the pitch too, as Suárez berated Downing for darting one way as the Uruguayan put an intended pass the other. Frequently attempted one-twos became one-nones. Their first chance of the match came from a Steven Gerrard free-kick to the back post, to which Martin Skrtel could not apply a telling connection. It took 25 minutes for Liverpool players to be sufficiently in tune with each other to truly threaten Wigan, Suárez and Downing finally exchanging cutting passes before the latter cracked a fierce low drive narrowly wide from a difficult angle 16 yards out.

Moments later, however, more Liverpool uncertainty led to the concession of a penalty. Jamie Carragher's attempt to clear a clipped Gary Caldwell cross resulted only in a weak back-header – Skrtel and Victor Moses challenged for it and the forward got there first, only to be inadvertently kicked in the head by the defender. Shaun Maloney fired the spot-kick past Pepe Reina.

Moses, meanwhile, was taken to hospital to be assessed. "He was concussed for a while and when he came around he was not really himself," said Martinez. "We are concerned it could be a fracture."

The mood among the Anfield faithful, meanwhile, threatened to turn from anxious to rebellious. During the 10 minutes that it took Wigan to decide to replace Moses, the visitors played with a numerical disadvantage that Liverpool could not exploit, long shots from Suárez and Gerrard being the best they could muster. Ali Al-Habsi dealt with both.

Dalglish introduced Andy Carroll for the second half as the hosts switched to 4-4-2. Within two minutes Liverpool were level thanks to their most vaunted duo. Suárez flipped a pass wide to Gerrard before getting it back again and doing what he has frequently failed to do this season – finish smartly, his low shot from 10 yards finding the corner of the net.

Liverpool thought Suárez had doubled his tally in the 54th minute but the referee ruled that he had turned the ball into the net from close range with his arm. Dalglish insisted it had brushed the striker's shoulder and the goal should have stood.

Then Liverpool lapsed back into lethargy. Wigan, who were compact and tenacious but rarely dangerous, regained the lead in the 63rd minute. James McCarthy's speculative shot from the edge of the area after another poor Liverpool clearance deflected off Carragher into the path of Caldwell, who showed unexpected deftness to sidestep Carroll, who had kept him onside, and slot the ball under Reina and into the net. "I think Gary surprised the whole Anfield crowd with his composure and he also surprised our whole bench," quipped Martinez. "But it is fitting that it was him because he is a leader, a rare breed. He has been through difficult times with us and always stood up so I am happy for him that his name is inscribed in our history with that goal."

Including stoppage time, Liverpool had half an hour to find an equaliser. They never looked like getting one. Suárez did bring a save from Al-Habsi in the 89th minute after collecting a flick-on from Carroll but that was a mere shower – there was no storm for Wigan to weather.