David Wotherspoon trudged off after receiving treatment just after the hour mark at Fir Park.
Another key midfielder, Murray Davidson, was already battling to be fit for next Sunday's Hampden clash with Livingston and missed the Fir Park trip.
Wotherspoon's premature exit was the only negative for manager Callum Davidson following an utterly dominant performance.
The second goal should have been disallowed for an offside but the controversy proved a footnote as Motherwell suffered more agony following the previous weekend's 4-1 home defeat by Hamilton.
Manager Graham Alexander lost four players following the derby humiliation with Stephen O'Donnell suspended, Bevis Mugabi injured and both Allan Campbell and Mark O'Hara missing through non-coronavirus illness.
Blackburn loan defender Tyler Magloire and 17-year-old full-back Max Johnston were handed their first starts and, with a number of pre-existing absences to contend with, there were two places unfilled on Alexander's inexperienced bench.
However, he will have major concerns about the way his team were completely outclassed – they only managed one shot at goal while the visitors produced 22 efforts.
There were only two points separating the teams before the game but the difference on the pitch was marked and Saints moved two points off the top six while Motherwell remain perilously close to the bottom two.
Motherwell struggled to get out of their own half before Melamed struck the opener in the 19th minute.
Saints looked far sharper and always seemed to have an option in possession while Motherwell struggled to get front three Christopher Long, Tony Watt and Devante Cole involved and barely got into the opposition box.
The visitors continued to threaten. Rooney came close with a powerful volley, Ali McCann screwed wide from a good chance after Motherwell had played their way into trouble, and Kerr headed just over.
The Perth men doubled their lead on the stroke of half-time after Liam Craig hit the underside of the bar from long range.
Rooney looked well offside as Chris Kane headed the rebound towards goal and the wing-back nodded the ball against the bar from close range. Assistant referee Colin McAlpine did not produce a flag and John Beaton gave the goal when Kerr thumped home the second rebound.
Any sense of injustice was quickly dampened as Saints went three ahead four minutes after the restart. Kane was too quick for Polworth as they challenged in the box and Melamed drove home the resulting penalty.
Wotherspoon and Callum Booth came close either side of the spot-kick and it was clear Alexander needed to change something.
They looked more solid but Craig hit the bar again from long range and substitute Stevie May forced a decent save from Motherwell goalkeeper Liam Kelly.