The message from Liverpool's principal owner was as succinct as it was apt. "Luis. Magician," tweeted John W Henry, diverting his attention from the Boston Red Sox's quest to win baseball's World Series to focus on his other sporting investment and a world-class footballer. Fittingly, there was a hat-trick for the Anfield illusionist, Luis Suárez, to defeat West Brom, even if he earned the match ball after Henry posted his thoughts online.

Nevertheless, it was an appropriate description. If magic involves an element of the imagination, Suárez certainly qualifies. He has a capacity to score goals others would not even conceive of attempting. The conjurer's greatest trick was to head in from 18 yards when the Albion goalkeeper, Boaz Myhill, had not left his line. It brought gasps of surprise and admiration in equal measure.

An overhead kick that the overworked Myhill tipped on to the bar was further evidence of his ability to execute the improbable. As magicians go, Suárez is more Harry Houdini than Paul Daniels – exotic and with a hint of danger – and Liverpool are reaping a reward after forgiving him for his various misdemeanours. Controversy, however, is a constant and arrived before the goals. Suárez tumbled to the turf when Gareth McAuley seemed to tug him. The referee Jonathan Moss deemed his fall overly theatrical and ignored his appeals for a penalty. Yet if Suárez felt he was wronged, he produced the right response.

He collected Kolo Touré's pass, beat Claudio Yacob, nutmegged Jonas Olsson with deceptive ease and slipped a shot beyond Myhill. "The first goal came from nothing," said Albion manager Steve Clarke, who has first-hand knowledge of Suárez's ability from his time as Kenny Dalglish's assistant at Anfield.

If Suárez's opener was excellent, his second goal was extraordinary. A player who specialises in doing the different contrived to score with a header from the edge of the area, an effort that flew past Myhill with the velocity of a well-struck shot. "I'm not sure he could have placed the ball in the top corner any better," added Clarke. Suárez played a part in the buildup, too, even if his under-hit pass meant Aly Cissokho's delivery was part cross, part tackle as Morgan Amalfitano slid in to challenge him.

Having advertised his aerial prowess, Suárez's hat-trick was completed with a second header. Steven Gerrard delivered the free-kick that the Uruguayan, escaping Victor Anichebe's attentions, met with a third precise but very different finish.

And yet, while a focus on Suárez is understandable, this was Liverpool's finest performance of the season. They had been criticised for winning without really impressing. Their excellence here was sustained for 90 minutes, as an in‑form Albion side can testify.

In a display of effervescent attacking, Daniel Sturridge oozed menace while Steven Gerrard was in commanding form. "Steven is a top, top, top, top, top player," said a smiling Rodgers, replying to Sir Alex Ferguson's claim in his autobiography that the Liverpool captain is not a "top, top player".

Sturridge, meanwhile, is the Premier League's top scorer. An eighth of the campaign was also his finest. He shrugged off Youssouf Mulumbu, spotted Myhill a few yards off his line and a placed an inch-perfect chip over the backtracking goalkeeper. "Sublime," said an admiring Clarke.

His current side had the misfortune to encounter the "SAS" at the top of their game. Both also hit the woodwork, Sturridge with a curling shot and Suárez with the acrobatic volley that Myhill pushed on to bar. Clarke's complaint was that Albion started too slowly.

"We gave ourselves a mountain to climb," he said. There were moments when they almost clawed their way up the slope. On the stroke of half-time, Martin Skrtel made a goalline clearance to prevent Nicolas Anelka, briefly a Liverpool player in 2002, from opening his Albion account. "Maybe if it goes 2-1, it is different," Clarke said.

Instead, after Suárez scored his third, they made it 3-1. James Morrison drove in a penalty after Billy Jones was challenged – seemingly cleanly – by Lucas Leiva, even if Cissokho may have been deemed the offender for an earlier trip. "I'm not sure about the penalty decision," admitted an honest Clarke.

He then headed off for a depressing coach journey on the M6, to be spent studying the DVD of the game. His departure was delayed when Anfield was evacuated after the final whistle when the fire alarm went off. It prompted the inevitable quips that West Brom should have set it off a couple of hours earlier.