Goals from Juvhel Tsoumou, Jamie Proctor and a controversial Danny Devine effort for the home side were ruled out by two from Wesolowski and Shefki Kuqi as the sides could not be separated.
Tsoumou gave Preston a 28th-minute lead, scoring his first home league goal when he headed home Danny Mayor's cross and Proctor doubled the four minutes later when he poked home Paul Coutts' cross from three yards out.
Kuqi pulled one back shortly before half-time when he beat the offside-trap from Wesolowski's pass to beat Preston goalkeeper Iain Turner, but Oldham equalised a minute before half-time after Wesolowski diverted David Mellor's free-kick past a stranded Turner.
Defender Devine put the home side back ahead in the 64th
minute with a long punt that went straight in, leaving the Oldham players complaining about a foul on goalkeeper Alex Cisak.
But Wesolowski levelled with four minutes remaining with a fantastic first-time drive from 20 yards out which flew past Turner and into the net.
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