Carrying a 11-5 lead into the final session, Stevens wasted little time finishing the job with runs of 22 and 38 allowing him to hold off Day's desperate attempts to salvage the session's opener in search of snookers with two balls on the table.
That was the Welsh Dragon's 10th successive frame in the tie, and number 11 booked his place in the final four courtesy of two visits at 36 and 41 apiece to prompt the handshake from Day.
Stevens, who has yet to taste glory at the Crucible despite reaching two finals, will meet either Ronnie O'Sullivan or Neil Robertson in the semi-finals.
Matthew Stevens won all eight second-session frames to lead Ryan Day 11-5 in their World Championship quarter-final at the Crucible.
The 2000 and 2005 runner-up carved out four 40+ breaks in as many frames to go from trailing compatriot Day by two frames after their first session to leading by that same margin.
A 44, a 48 and two 46 breaks turned the last eight encounter around, but Stevens was not done and won the following four after the interval to make it nine consecutive frames and leave Day staring the exit door in the face after looking strong earlier in the day.
Stevens finished the night with a 63 which left him two frames away from the semi-finals in Sheffield.
Ryan Day took a 5-3 lead in frames after the first session of his World Championship quarter-final against former finalist Matthew Stevens.
Day had lost the opening frame after a run of 86 from the two-time former finalist, but insisted on coming to the table for a couple of pots anyway and he soon put the extra table time to good use.
Two quick-fire centuries soon put him ahead against his fellow Welshman, and though Steven's 49 ensured the two were all square going into the mid-session break, Day kept his form strong in the closing four.
Day made a break worth 80 in the fifth and withstood a barrage of Stevens snookers to lead 4-2, before guaranteeing a first-session lead with a 57 break for his third on the bounce.
Stevens, favourite to advance to the last four at The Crucible, edged his way to the eighth to stop the rot and keep within two frames, though a rattle from the final green before it dropped provoked gasps from the crowd and Matthew himself.
The two resume their last-eight encounter from 7pm.