The Broncos have failed to collect a single point all season but they led 10-4 leading into the final quarter of the match after first-half tries from Matt Cook and Thomas Minns.
But Wildcats forward Daniel Smith crashed over in the 65th minute and Matt Ryan added a late clincher to make it 18-20 and leave Joe Grima’s side heartbroken.
While London remain rooted to the foot of the table on zero points, new Wakefield coach Webster saw his side move eight points clear of Bradford to take a step closer to safety.
Australian boss Webster, who recently replaced Richard Agar, thrust the returning Tim Smith straight into the starting line-up and paired the Australian with Paul Sykes in the halves.
Smith left Wakefield for Salford last August but has failed to settle with the Red Devils and rejoined the Wildcats on loan for the rest of the season earlier this week.
As the match kicked off, the rain began to fall and both sets of players were soon drenched, which made for difficult conditions and a physical battle between the forwards.
After a knock-on by the Broncos inside their own half, Wakefield had the opportunity to build pressure on their visitors and they took with an opening try in the 10th minute.
The Wildcats drove forward and Tim Smith’s deft offload sent skipper Danny Kirmond crashing over the line from 10 metres out inside the right channel.
Sykes failed to add the conversion but London steadied themselves and forced Wakefield to drop out from under the posts shortly after.
Yet the Broncos knocked on again immediately from the drop-out and were forced onto the back foot once more.
But they battled doggedly and hit back with two tries in three minutes to lead 10-4.
First they struck in the 19th minute when a teasing kick behind the Wakefield defence was not dealt with and Matt Cook pounced on the loose ball to touch down.
Minutes later, Atelea Vea broke clear and, although his progress was halted 10 metres, the Broncos worked the ball into the right corner where Minns grounded Nesiasi Mataitonga’s short kick.
Those two tries visibly poured confidence into the visiting players and they spent the remainder of the first half camped in Wakefield’s half.
They should have had a third shortly before the break when George Griffin broke clear and passed to Mason Caton-Brown, who was hauled down.
Wakefield improved markedly after the restart but they struggled badly to make it pay and Josh Drinkwater’s fine tackle halted Matt Ryan’s progress as he threatened to burst clear on the hour.
In the 63rd minute, Lucas Walshaw broke down the left flank and, although Iliess Maccani made a superb saving tackle, Wakefield worked the ball across the London defence and Daniel Smith crashed over from close range.
Sykes converted to level the scores at 10-10 and then kicked a penalty to edged Wakefield in front before he added another conversion after Ryan touched down after a kick from Richie Mathers was spilled by the London defence.
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