Goals from central defender McShane and striker John Hartson in the opening 15 minutes set up Albion to see off the challenge of Leeds, who now only have a Championship survival fight to look forward to for the rest of the season.
Striker Kevin Phillips set the seal on the win eight minutes from time when he converted a Jason Koumas cross for his ninth goal of the season.
All Leeds had to show for their efforts was an injury time own goal from Albion left-back Paul Robinson.
The victory continued Albion's impressive run of form at the Hawthorns where they have won 12 of their 16 league and cup games this season.
McShane, who joined Albion from Manchester United in August, set them on their way in the sixth minute before Hartson took his tally for the campaign to six.
Leeds paid the price for a woeful first-half display – summed up by the fact that manager Dennis Wise used all three of his substitutes at half-time. He hauled off Matt Heath, Ian Moore and Jonathan Howson sending on debutants Tore-Andre Flo and Armando Sa and Shaun Derry.
Promisingly for Leeds, the front line pairing of former Chelsea marksman Flo and David Healy did look like one that could be effective in their battle to avoid relegation.
Flo was particularly impressive without getting the reward that his play deserved - seeing his point blank drive saved by Russell Hoult in the 81st minute as Leeds produced a much improved second-half display.
But the damage had been done by then as Leeds crashed to their second defeat of the season at the Hawthorns having lost 4-2 in the league in September.
Leeds can take solace from the fact they did not buckle completely and only some smart play by Hoult denied them a route back into the game.
But Albion, who also hit the bar through Diomansy Kamara in the 68th minute, proved too quick for Leeds in the opening exchanges.
The writing was on the wall for them when Robbie Elliott cleared Koumas' shot off the line. It proved a brief escape as, from the resulting corner, Neil Clement's cross was converted by McShane with a low drive.
Leeds were still reeling from that setback when Hartson struck. A long clearance from Hoult flew to Hartson who powered his way past Heath before drilling his low shot through goalkeeper Neil Sullivan.
To their credit, Leeds rallied and would have got a foothold in the match but for Hoult. The veteran 'keeper saved a free-kick from Eddie Lewis and a shot from Robbie Blake before Sullivan prevented Hartson grabbing his second with a smart one handed stop.
But it was Hoult who was the busier 'keeper. In the 34th minute he beat away Blake's rising drive before spectacularly tipping a volley from Kevin Nicholls round the post 60 seconds later.