However, it was Morgan’s all-round display and not just his goals, which underlined why Celtic manager Brendan Rodgers is so keen to add him to his squad.
A £500,000 move could be agreed as early as next week, although, understandably, there are suitors down south who would also like to sign him.
Saints manager Jack Ross had admitted earlier in the day that the match could be postponed but, thanks to the efforts of dozens of volunteers, referee Don Robertson passed the pitch as playable.
Nine minutes of fairly frantic action had elapsed before either goalkeeper was called into action, United’s Harry Lewis requiring two attempts before holding a half-volley from Jack Baird which had come through a ruck of players.
United spurned a glorious opportunity to take the lead just three minutes later when Ian McShane appeared to take the feet from Andy Durnan as both players attempted to attack a Billy King corner.
Paul McMullan took the resulting penalty but it was at a good height for Craig Samson, who stretched to his right and pushed it away.
The wind and driving sleet made for difficult conditions on a slippery surface. Mr Robertson may have factored that into his decision not to penalise Kyle Magennis for a lunge at McMullan and Scott McDonald may have attempted to use it as an excuse for the late challenge on Baird which earned him a caution.
Paul Quinn did have the ball in the net with a firm header from another King set piece but the whistle had gone for an infringement just before the centre-back made contact.
Saints were almost the architects of their own downfall again just before the interval when Liam Smith was dispossessed by Sam Stanton 40 yards from his goal. The latter supplied Scott Fraser, who had time to take a touch but still failed to hit the target from the edge of the penalty area.
Fraser had to duck to avoid snowballs thrown by the home fans as he attempted to take a corner which proved to be no more accurate than the aforementioned frozen missiles.
United manager Csaba Laszlo was ready to replace Willo Flood in the 53rd minute after his captain had injured himself making a goal-saving tackle on Daniel Mullen.
Matthew Smith was stripped and the number boards were readied but Flood indicated that he would carry on.
Stanton became the next player to be cautioned, for a foul on Morgan, but the game was crying out for a spark of quality and it arrived in the 59th minute from Morgan.
The midfielder collected a short free-kick from McShane and turned inside before beating Lewis with a peach of a right-foot shot from 20 yards.
Smith eventually replaced Flood ten minutes after he had expected to but United had lost the momentum they had built up earlier and the home side looked more likely to increase their lead than surrender it.
That proved to be the case when Morgan notched his second in similar fashion to the opener. This time he lost the ball after McShane had again supplied him but he was alert when Stephen McGinn’s incisive pass found him, driving first time past Lewis. Understandably, he left the field to a standing ovation when substituted in the final moments.