Robin van Persie struck an injury-time winner as Arsenal dealt Liverpool's hopes of Champions League qualification a shattering blow with a 2-1 victory at Anfield on Saturday.

Dutch international van Persie volleyed home magnificently in the third minute of stoppage time to claim his second of the match and take his season's tally to 31 in all competitions.

Van Persie's last-gasp winner saw Arsene Wenger's side cement their grip on fourth place, and moved the Londoners to within four points of third placed Tottenham who play Manchester United on Sunday.

But the defeat has left Liverpool with a mountain to climb if they are to secure a return to Europe's elite next season, with 10 points now separating them from Arsenal in fourth.

Arsenal just ‘got lucky’

Van Persie admitted Liverpool had been unlucky to lose.

"I don't think we deserved it if I'm being honest because Liverpool played better but to nick it like we did – we can only be pleased," the striker said.

"We are 10 points ahead of Liverpool now and Spurs play tomorrow against Man Utd. We will have to wait and see. It is a big win, a massive win."

Arsenal boss Wenger hailed the contribution of his match-winning striker.

"When you see the ball land at the feet of Van Persie you know what he can do," Wenger said. "We cannot afford to lose him. Overall you have to give him credit because in every match he does something special.

"Maybe we were a bit lucky to get the three points today but it gets us away from Liverpool and we are on a good run now."

Champions League next

Wenger said the victory would give Arsenal belief as the attempt to overturn a 4-0 first leg deficit over AC Milan in the Champions League on Tuesday.

"It puts us in a good condition to make the impossible possible against Milan," he said.

Liverpool played well, but…

Liverpool manager Kenny Dalglish was struggling to come to terms with defeat after a match which saw the Reds miss their sixth penalty of the season and a string of clear scoring opportunities.

"It's difficult to believe but that's the way it goes, we played some fantastic stuff and came away with nothing," Dalglish said.

"The scoreline doesn't reflect the game. We showed what we are capable of in the first half.

"We were beaten because we didn't score enough goals. We should have had enough that their two goals wouldn't matter. But Van Persie is a fantastic footballer there is no doubt about that.

"We will keep going. We will add the points up at the end of the season and see where we finish."

What the match was all about

The defeat was cruel on the Merseysiders, who had dominated throughout only to be denied by a string of superb saves from Arsenal goalkeeper Wojciech Sczesny and the woodwork.

Polish international Szczesny had needed to be alert from the outset, reacting swiftly in the 10th minute to snuff out a break from Luis Suarez before dealing with a follow-up from Stewart Downing.

Szczesny then pulled off a superb double save as Liverpool missed from the penalty spot after the Arsenal keeper was adjudged to have brought down Suarez following a neat one-two with Dirk Kuyt.

It was only a temporary reprieve however as Liverpool took the lead on 23 minutes, Arsenal defender Laurent Koscielny turning Jordan Henderson's whipped low cross into his own net past Szczesny.

But Arsenal were back on level terms in the 31st minute with their first genuine effort of the game, van Persie heading in from Bacary Sagna's cross.

Liverpool struggled to carve out as many clear chances after the break but the Reds did squander a golden chance to go ahead on 70 minutes.

Kuyt crossed from the right to find an unmarked Martin Kelly only for the defender to miskick from point-blank range with the goalmouth gaping.

A draw seemed the likeliest result but deep into injury time - provoked by a second-half injury to Mikel Arteta - Alex Song chipped into the Liverpool area and van Persie volleyed home on the full to clinch a dramatic win.

Chelsea go down, City fetch another win

West Bromwich Albion piled the pressure on Chelsea with a 1-0 victory on Saturday as Premier League leaders Manchester City downed Bolton to open up a five-point lead at the top of the table.

An 82nd minute strike from Gareth McAuley secured all three points for West Brom at the Hawthorns to deal a fresh blow to under-fire Chelsea manager Andre Villas-Boas, reportedly battling to hang on to his job.

The defeat left Chelsea three points adrift of the top four after Arsenal's push for Champions League qualification was given fresh momentum following a dramatic 2-1 win over Liverpool.

Chelsea's points haul of 46 after 27 games is their lowest at this stage of the season since the 2001/2002 campaign.

City smooth on top

Elsewhere, leaders City cruised to a 2-0 win over Bolton courtesy of an own goal from Gretar Steinsson and a strike from Mario Balotelli.

The win preserved City's 100 per cent home record and left second-placed Manchester United needing to get a result at Tottenham on Sunday to reduce their rivals' lead at the top.

City manager Roberto Mancini meanwhile confirmed that goalscorer Balotelli could face disciplinary action after being photographed leaving a Liverpool strip club in the early hours of Friday morning.

"I will speak to him tomorrow before deciding about the maximum fine I will do," Mancini said. "I'm really disappointed. I will stick with him because he's a good player but I will speak to him about the fine."