Full-time from The Den
Morison was on hand to calmly slot home from the penalty spot 10 minutes after coming on as a sub to add to Jimmy Abdou's 62nd-minute opener for The Lions.
It proved to be a routine win for Neil Harris' side, who were never really troubled by a young and energetic Baggies outfit not lacking in effort, but without the quality or composure of their opponents.
Boss Harris handed first senior starts to Kris Twardek and Noah Chesmain, taking to eight the number of players in the starting XI who have at some stage come through the ranks at The Den. It was nine in all, with the second-half appearance of sub Ben Thompson.
Left-back Chesmain soon got the crowd on their feet with a crunching fifth-minute tackle deep in his own half as The Lions started with real intent.
Philpot was a whisker away from connecting with Gregg Wylde's flat delivery and then a stinging long-range effort from Chesmain hit Shaun Donnellan full-on in the face in the opening quarter of an hour as Millwall pressed.
A nice passage of play between Wylde and Aiden O'Brien saw both players dip into their box of tricks with neat back heels before a promising move down the left broke down, but the opening half failed to really ignite with neither side creating any clear chances on goal.
The visitors found it tough to make any headway against a Millwall rearguard well-marshalled by Tony Craig, and on the one occasion they did threaten, James Smith sent a header over the bar after Kane Wilson's pass had been flicked into his path by Donnellan.
West Brom brought on Zak Elbouzedi for Donnellan at the break, but it was The Lions who drew first blood on 62 minutes with a smashing goal from Abdou. The midfielder worked his magic, shimmied into the penalty area, held off a defender and dispatched a low shot that gave Jack Rose no chance in the visiting goal.
Three minutes a triple change by Lions boss Harris proved decisive and by the 75th-minute, Morison's goal had effectively put the game to bed.
Morison had already gone close with a lofted effort that dropped onto the roof of the net and seen a low shot hacked clear by right-back Kane before adding his sixth goal of the season.
Fellow sub Thompson burst into the penalty area and when Dara O'Shea was deemed to have fouled The Lions midfielder, up stepped Morison to calmly dink the resulting penalty beyond the reach of Rose.
Morison had another chance to add to his tally, heading a corner from Wylde straight into the hands of the keeper who made a comfortable save.
Tuesday's results in Group H - a 2-1 win for Luton at Gillingham - leaves The Lions top with a home game against The Gills next up for Millwall in the competition on Tuesday 4th October.
Scorers: Abdou (62mins), Morison (75mins, pen)
West Brom: Rose, Wilson, McCourt, Donnellan (Elbouzedi, 46mins), Fitzwater (Piggott, 88mins), O'Shea, Sweeney, Smith (Pritchatt, 78mins), Wright, Harper, Nabi. Subs not used: Palmer, Wilding, Forss, Melbourne.
Att: 2,054 (away 81)
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