Tournament favourite O'Sullivan made a slow start to the evening as Stevens picked up the opening two frames including a break of 82.
O'Sullivan's looked frustrated when he missed a red in the third frame as he thumped his cue of the side of the table.
The cue visibily wilted, but did not snap as O'Sullivan returned to the table to make a quickfire 100 in reducing the deficit to 2-1.
English Open
Perfect safety shot from Yuan Sijun
He would proceed to snare the next four frames with breaks of 63 and 61 in the fifth and sixth frames.
O'Sullivan managed to pinch the seventh frame for a 5-2 lead despite Stevens making 55, but the Welshman finished with a 71 to trail by two before Sunday afternoon's second sesson.
REPORT: Ding Junhui ousts John Higgins with Stuart Bingham also into last eight
In the other action of the evening, 2013 finalist Barry Hawkins recovered from trailing 9-6 and 11-8 to complete a rousing 13-11 win over Mark Allen.
The turning point came in the 17th frame when Hawkins escaped from a snooker to trail 9-7 before the final session.
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Latest last 16 results (best of 13 frames)
Mark Selby (Eng) 9-13 Anthony McGill (Sco)
Joe Perry (Eng) v Shaun Murphy (Eng)
Barry Hawkins (Eng) 13-11 Mark Allen (NI)
Ali Carter (Eng) 2-6 Neil Robertson (Aus)
Ding Junhui (Chn) 13-9 John Higgins (Sco)
Marco Fu (HK) v Judd Trump (Eng)
Graeme Dott (Sco) 5-13 Stuart Bingham (Eng)
Matthew Stevens (Wal) 3-5 Ronnie O'Sullivan (Eng)
Quarter-final draw
Anthony McGill (Sco) v Joe Perry (Eng) or Shaun Murphy (Eng)
Barry Hawkins (Eng) v Ali Carter (Eng) or Neil Robertson (Aus)
Ding Junhui (Chn) v Marco Fu (HK) or Judd Trump (Eng)
Stuart Bingham (Eng) v Matthew Stevens (Wal) or Ronnie O'Sullivan (Eng)
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