But despite controlling the game and having 72% possession, the hosts failed to put the game beyond reach. Ultimately they were punished for their lack of efficiency in front of goal, as Ajayi rose highest to head the leveller beyond Alisson.
You could be forgiven for starting to think Liverpool will never lose a Premier League game at Anfield again as the Reds completed a third calendar year without defeat on home soil and extended their lead at the top to three points.
Klopp will have been disappointed that his side only led by a single goal at the break despite registering 84% possession, and they paid the price for failing to put the visitors to the sword as Ajayi headed the equaliser via both posts.
Manager rating out of 10
5 -- It's the season of giving and the German received a yellow card for a slightly overzealous reaction to a free kick awarded against his side. If he was angry then, it's probably nothing compared to how he felt when West Brom equalised.
Player ratings (1-10; 10 = best. Players introduced after 70 minutes get no rating)
GK Alisson, 6 -- The Brazilian had little to do for large spells, but stayed on his toes and produced a big save to deny Karlan Grant who had burst clear of Rhys Williams. Despite that, the scrambling keeper was beaten by Ajayi's towering header.
DF Trent Alexander-Arnold, 7 -- After a quiet opening 10 minutes, the right-back started to move through the gears and caused chaos in the visitors' penalty area with a couple of dangerous deliveries.
DF Joel Matip, 7 -- Showed the level of authority his manager will have been looking for from the off, camping himself on the halfway line. He helped himself to a rare assist too, picking out Mane who made no mistake from close range.
DF MF Fabinho 6 -- The midfielder by trade has proven to be more than capable at centre-half. Like Matip, he pressed high and penned the visitors inside their own half, but he fired comfortably over the bar from just outside the box.
DF Andrew Robertson, 7 -- Twice breached the visiting backline in the early exchanges with a couple of perilous low crosses somehow evading everyone at the back post.
MF Jordan Henderson, 7 -- Liverpool just seem much more relaxed with him in the side. The skipper dictated the play from the middle and almost helped himself to a second goal in as many games with a curling effort just after the restart.
MF Georginio Wijnaldum, 5 -- Found himself having to do a rare bit of defending when he blocked Romaine Sawyers effort, although the flag went up anyway. Otherwise a quiet performance from the Netherlands international.
MF Curtis Jones, 6 -- The 19-year-old has impressed the season and he seems to have an ability to glide through midfield and find a pass. He produced another assured display against a visiting side who were happy to try and soak up pressure.
FW Mohamed Salah, 6 -- Liverpool's talisman was unplayable at Fulham and came into this one chasing his 10th goal in just 13 games. He lacked his usual ruthlessness in spells, first failing to connect with Robertson's cross before heading over from a corner.
FW Roberto Firmino, 7 -- Firmino has been firing again of late with three goals in his previous two games. He came desperately close to another too with a downward header that drew an excellent save from Sam Johnstone and showed his usual flair in some tidy link-up play.
FW Sadio Mane, 7 -- It took less than 12 minutes for the forward to open the scoring, neatly chesting down Matip's ball forward before steering past the helpless Johnstone. Almost doubled his tally when he headed Henderson's cross narrowly wide.
DF Rhys Williams, 5 -- Replaced Matip in the 59th minute but he couldn't match the pace of Grant who raced onto a ball over the top only to be denied by Alisson. Later conceded the corner which led to West Brom's equaliser.
MF Alex Oxlade-Chamberlain, N/R -- 'The Ox' replaced Curtis Jones and wasted no time in getting involved in the action, but the twisting and turning midfielder couldn't find the target.
FW Divock Origi, N/R -- Replaced Firmino just seconds after the striker had come so close to restoring the Reds' lead but didn't really have time to make an impact.