Wednesday took the lead through Deon Burton's 17th-minute penalty when Glenn Whelan was tripped by Jim Goodwin.
Almost immediately the visitors drew level after defender Andy Butler guided a header at the far post back across goal and Paterson stab the ball in.
And just before the break Cleveland Taylor broke down the right, and his low cross was thumped in by Paterson.
Scunthorpe boss Nigel Adkins on Brian Laws
"It's about sticking together through the hard times and if the right person is in place you stand by him. "He should remain manager at Sheffield Wednesday. He's a good one.
"It's a volatile environment. People want immediate success. But I know it's a results-based business like I'll find out when we start losing matches."
Sheff Wed: Grant, Hinds, Wood (Bullen 35), Michael Johnson, Spurr, Whelan, O'Brien (Esajas 76), Jermaine Johnson, Kavanagh, Tudgay, Burton (Sodje 46).
Subs Not Used: Burch, Lunt.
Goals: Burton 23 pen.
Scunthorpe: Murphy, Crosby, Butler, Byrne, Youga, Taylor, Hurst, Goodwin, Sparrow (Williams 81), Hayes (Forte 72), Paterson (May 85).
Subs Not Used: Lillis, Iriekpen.
Booked: Butler, Youga, Crosby.
Goals: Paterson 24, 40.
Att: 21,557
Ref: Anthony Taylor (Greater Manchester).
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