Late points from Keelan Sexton and Manus Doherty secured Clare's place in the last 12 of the All-Ireland SFC in Cusack Park, Ennis, as they got past a dogged Meath by 1-11 to 1-09.
Having led by four points at half-time with the wind to come, nothing but a home victory appeared on the cards.
However, a combination of poor shooting (eight second-half wides) and two outstanding late saves from Meath goalkeeper Harry Hogan including a 63rd-minute penalty stop from David Tubridy left the door ajar for the visitors to prosper.
Full-back Conor McGill stepped forward to convert a 40th-minute penalty for his first ever score for Meath while successive points from Daithi McGowan and Bryan McMahon inched the Leinster side in front for the first time by the turn of the final quarter at 1-08 to 1-07.
Indeed, it had to take the intervention of Clare captain Eoin Cleary to peg back a resurgent Meath on two occasions before substitute Sexton and corner-back Doherty completed a Banner victory.
It was all so different early on when Clare points from Eoin Cleary and Emmet McMahon sandwiched a 12th-minute goal when Cleary's effort for a point dropped short and Pearse Lillis was quickest to react to flick to the net.
Lillis might have doubled his bounty only four minutes later only for goalkeeper Hogan to excellently parry his point blank attempt at 1-03 to 0-00.
It took wind-assisted Meath 18 minutes to open their account through Thomas O’Reilly but Clare responded with three of the next four points to carve out a 1-06 to 0-02 advantage by the 27th minute.
Jack O’Connor, Jason Scully, Eoin Harkin and Cillian O’Sullivan all chipped in with late points to lower the half-time arrears to just four at 1-07 to 0-06.
And with Clare starting to falter in front of the posts on the resumption, it seemed as if Meath’s hoodoo over Clare would extend to a sixth victory in only five seasons when completing a full recovery only eight minutes into the new half.
Experienced duo Bryan McMahon and Cillian O’Sullivan twice nudged their side in front entering the final quarter, only for Eoin Cleary to negate both.
So despite Hogan’s subsequent goalkeeping heroics to tip away a Tubridy penalty as well as a Keelan Sexton bullet, Clare stuck to their task to finally get over the line with the last two points.
Clare: Tristan O’Callaghan; Manus Doherty (0-01), Cian O’Dea, Conor Jordan; Alan Sweeney, Ciaran Russell, Jamie Malone (0-01); Darren O’Neill (0-01), Cathal O’Connor; Pearse Lillis (1-00), Eoin Cleary (0-04, 0-02f), Emmet McMahon (0-02); Gavin Cooney, David Tubridy (0-01, 0-01f), Aaron Griffin
Subs: David Sexton for O’Callaghan (5-13, BS), Keelan Sexton (0-01, 0-01’45)for Griffin (34), Brendy Rouine for McMahon (46), Podge Collins for Cooney (49), Cillian Rouine for Sweeney (67)
Meath: Harry Hogan; Robin Clarke, Conor McGill (1-00, 1-00 Pen), Eoin Harkin (0-01); Cathal Hickey, Pádraic Harnan, Donal Keogan; Bryan Menton, Daithi McGowan (0-01); Jason Scully (0-01), Thomas O’Reilly (0-01), Jack O’Connor (0-01, 0-01f); Mathew Costello (0-01), Cillian O’Sullivan (0-02, 0-01m), Bryan McMahon (0-01, 0-01f)
Subs: James McEntee for Hickey (24), Eamon Wallace for O’Connor (HT), Joey Wallace for Scully (HT), Jordan Morris for McMahon (59), Shane Walsh for O’Reilly (67)
Referee: Brendan Cawley (Kildare)