Wednesday's day could not have got off to a worse start as Joel Ndala's awful clearance with just over a minute on the clock landed at the feet of Hamer 30 yards out, and he slid in Bamford to score with a calm finish.
It could have been 2-0 soon after when Callum O'Hare drove forward and hit a shot that struck the outside of the post, and Japhet Tanganga crashed a shot over the bar after a neat free-kick routine.
United did double their lead when Bamford and Peck linked up neatly before the latter sent Burrows in on goal to finish with aplomb.
Thereafter, they cruised through to the break, something that they were nearly made to pay for in the hectic 40 minutes that followed Phillips' red card.
The Owls' depleted numbers were further hampered by veteran defender Liam Cooper and Crystal Palace loanee Tayo Adaramola going off injured.
They travel to Norwich City on Wednesday night aiming to avoid a Championship record 11th straight defeat.
They are also in danger of breaking a number of other EFL records, including the fewest goals in a season, the fewest wins in a 46-game season, and becoming the first team to go a whole season without a home win.