Millwall 2 Barnsley 0: Barnsley briefly threaten but are undermined by first-half double
The Wales striker gave any Premier League clubs looking for a goalscorer before the transfer window shuts another nudge with his 17th-minute strike.
The Lions are desperate to hold onto their top scorer, who has been linked with Fulham and Wolves, and hope to tie him to a new contract.
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Hide AdBut manager Kenny Jackett may be tempted to switch his phone off between now and Monday evening just to be on the safe side.
James Henry added a second before half-time as Millwall moved up to eighth, just three points shy of the top six. It all added up to a second wasted trip to south London in the space of a month for Barnsley fans after the original fixture was called off a couple of hours before kick-off.
Their team nearly gave them something to cheer in the 15th minute but Hugo Colace fired over from 12 yards.
However, Millwall dominated the first half and went ahead two minutes later when Henry's low cross found Morison all alone at the far post to tap the ball home.
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Hide AdBarnsley briefly threatened again when Colace was put through but his chip was comfortably dealt with by goalkeeper David Forde.
And the Lions went 2-0 up in the 37th minute when Henry's 20-yard drive took a huge deflection off Tykes full-back Matthew Hill, wrong-footing Luke Steele.
Morison should have made it three when Liam Trotter sent him through one-on-one with Steele, but his first touch let him down.
Barnsley livened up after the break and Danny Haynes, who scored twice on his debut in Tuesday night's win at Doncaster, fired a decent chance wide.
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Hide AdAt the other end Morison had a shot bravely blocked by Jason Shackell before teeing up Henry who could only divert the ball over with his knee.
Jacob Butterfield might have dragged Barnsley back into the game with 10 minutes left but their chances disappeared with the midfielder's shot as it flew wide.
Millwall: Forde, Dunne, Barron, Purse, Mkandawire, Eastmond (Harris 70), Abdou, Schofield, Trotter, Henry, Morison. Unused substitutes: Mildenhall, Hackett, Smith, Lisbie, Theo Robinson, Marquis.
Barnsley: Steele, Shackell, Hassell, Trippier, Hill, Butterfield (Taylor 84), Doyle, O'Brien, Colace (Arismendi 71), O'Connor (Bennett 74), Haynes. Unused substitutes: Preece, Lovre, Branson, Gray.
Referee: Graham Scott (Oxfordshire).
jacoB butterfield: Missed late chance which would have given Barnsley some hope of a point.