Little had been booed off after Villa struggled to beat Portsmouth in their third-round replay and then came last week's five-goal defeat by Blackburn. The transfer listing of the disgraced Yugoslav striker Savo Milosevic soon followed after an alleged spitting incident.
So an upset was in the air, even though West Brom have hardly set the First Division alight, and the pens were readily sharpened in the packed press box. But Little spared no energy in rejuvenating his players for this rare derby.
Within three and a half minutes of the start, Simon Grayson repaid his manager's efforts by blasting Villa into the lead. Second-half goals from Dwight Yorke, who scored twice in three minutes, and Stan Collymore capped a convincing all-round performance and it is little wonder that the Villa fans broke into a chorus of "Can We Play You Every Week?"
Little said: "Our Premiership form has to improve if we are going to achieve anything this season. It will not help us in the cups if we are struggling to find form in the league. But I'm happy - this game was all about the result and we got it."
Grayson's all-important, nerve-settling goal stemmed from a Steve Staunton corner which was half-cleared and then knocked back in by Lee Hendrie. Grayson was first to react and shot powerfully past Alan Miller.
That prompted the start of some excellent football from Villa against a stunned Albion side. Hendrie and Mark Draper both went close before half-time, while Collymore clipped a delightful shot over the goalkeeper only to see it strike the crossbar.
Albion were reduced to the occasional, hopeful long-range shot but found a new gear after the interval, no doubt helped by the manager Denis Smith's half-time talk. They matched and even outplayed Villa for 15 minutes and nearly equalised when a 20-yard Lee Hughes shot was tipped over the bar.
But any comeback hopes disappeared in the 61st minute when Yorke struck the first of a quick double. He took a pass from Gary Charles, timing his run to perfection to avoid the offside trap, and then wriggled his way through Albion's central defenders before stabbing the ball past Miller from eight yards. His second goal, three minutes later, was better: Yorke, receiving a pass from Grayson on the edge of the area, turned the defender Shaun Murphy inside out before hitting a left-foot shot into the top right- hand corner.
The fourth goal was a luxury, but how the Villa supporters love it when Collymore scores, having an appreciation of rare and costly artistry as they do. He controlled the ball wide on the left and then cut into the area to beat the keeper at his near post. He celebrated in front of the Albion fans but, by then, there were not that many of them left.