Foxes chief Eriksson made four changes from the team which grabbed a 2-2 draw against Leeds on Boxing Day, but his reshuffle failed miserably as his side were outplayed in south London.
Wales striker Morison took his tally for the season to 11 and Puncheon grabbed his second goal since joining on loan from Southampton to leave the visitors on the ropes well before half-time.
Sven's men fought back from two goals down to snatch a point from Leeds, but showed little sign of a repeat performance despite playing against 10 men for more than half an hour following Alan Dunne's dismissal as they slumped to a ninth defeat on the road this term.
Millwall led when Liam Trotter crossed from the right and Morison was on hand to fire into the net.
The Lions had their tails up and continued to attack, and they deservedly went two ahead after 25 minutes when City defender Jack Hobbs was caught napping and Puncheon nipped in to prod Tony Craig's ball past Chris Kirkland.
Source: PA
Source: PA