Substitute Barry McBennett struck the decisive goal, and 1-02 in all, as Monaghan ended their lengthy barren streak with a vital win to prolong their interest in the All-Ireland SFC.
A first competitive win since beating Dublin in the opening round of the Allianz League in January secured third position in the Group 4 table for Vincent Corey's side.
It might have been even better as Monaghan were only nudged into third position in the table by Louth on scoring difference.
Monaghan led by nine points at the hour mark and at that stage were eyeing second position and a home preliminary quarter-final next weekend.
But a late Meath rally which yielded seven points in a row for the Tailteann Cup holders brought the margin down to just three points at full-time - and Louth ultimately finished three points better off than Monaghan in the table.
That will be a slight frustration for Monaghan supporters as they will be away from home next weekend but after so long without a win, their mood will surely remain positive.
Last year's All-Ireland semi-finalists had nine different scorers in all including free-takers Jack McCarron and Micheal Bannigan who sniped 0-07 between them while All-Star Conor McCarthy excelled again too.
Ryan O'Toole (arm) and Joel Wilson (head) picked up injuries which may hamper them in terms of next weekend's preliminary quarter-final.
Meath's fourth consecutive defeat has ended their season, though manager Colm O'Rourke signalled immediately afterwards that he intends to stay on for 2025.
It was a collision of contrasting styles in Cavan with a couple of heavy downpours, particularly one before throw-in, greasing up the pitch and adding to the early intrigue.
Meath opted to concede the Monaghan kick-out, partly to allow themselves to reset defensively but probably also to restrict Rory Beggan's ability to pick out men with long deliveries.
Beggan still got involved in the play as a sweeper 'keeper and was typically to be found as their anchorman up around the halfway line.
But it's a risky strategy when things go wrong and on four separate occasions in the first-half, Meath won back possession and ran hard at Monaghan who were left badly exposed with Beggan miles from home.
Meath harvested 1-01 off those turnover attacks, the goal coming from Cathal Hickey in the 22nd minute.
Monaghan defender Jason Irwin misplaced a kick-pass across midfield, which Jordan Morris ate up, beginning a dashing move that involved Conor Gray and Mathew Costello and ended with Hickey lashing past Beggan who had only just got back to man his goalline.
Three minutes later, Meath did something similar with a Sean Coffey ball over the top of Monaghan's pushed up defence free full-back Adam O'Neill of all people to bear down on goal. Monaghan just about got back on this occasion but Ryan McAnespie still had to foul O'Neill, allowing Costello to chip over a handy point.
That score left Meath 1-04 to 0-05 up as they bounced back from a slow start but just as they appeared to be gaining a foothold in the game, they relinquished it again.
Three Monaghan points in a row from Micheal Bannigan and Killian Lavelle left the Farney with a 0-08 to 1-04 half-time lead and eyeing a rare victory.
What appeared to be shaping up as a terrific second-half turned out to be a damp squib as Monaghan brought their greater craft and experience to bear.
They outscored Meath by 0-08 to 0-02 in the first 20 minutes of the second-half to effectively tie up the win with a 0-16 to 1-06 lead at that stage.
Stephen O'Hanlon, so good for Monaghan on the night they won their last game in late January at Croke Park, came alive with two great points in the third quarter. McCarthy added to this tally too before McBennett struck a 59th minute goal that killed the contest.
Bannigan freed McBennett with the pass through the middle and the sub drove powerfully beyond Hogan to the net.
Meath, to their credit, refused to relent in the closing stages and reeled off those seven points in a row to leave Monaghan not so much fearing for their scoring difference but wondering if the result might go the Royals' way.
Eoghan Frayne and James Conlon were excellent in this period but Meath just came up short with Monaghan sub Conor McManus hitting an insurance point from a free at the death.
Monaghan: Rory Beggan; Jason Irwin (0-01), Killian Lavelle (0-01), Ryan Wylie; Ryan McAnespie, Ryan O'Toole, Conor McCarthy (0-02); Gary Mohan, Joel Wilson; Michael Hamill, Micheal Bannigan (0-03, 0-02f), Stephen O'Hanlon (0-02); Andrew Woods (0-01), Jack McCarron (0-04, 0-04f), Ciaran McNulty.
Subs: Barry McBennett (0-01) for Wilson 2-6 blood, McBennett (1-01) for Wilson 29, Thomas McPhillips for O'Toole 51, David Garland for McNulty 55, Conor McManus (0-01, 0-01f) for McCarron 59, Micheal McCarville for Hamill 67, Stephen Mooney for Woods 71.
Meath: Billy Hogan (0-01, 0-01 45); Donal Keogan, Adam O'Neill, Ronan Ryan; Ciaran Caulfield, Darragh Campion, Sean Coffey; Cathal Hickey (1-00), Conor Gray; Sean Ryan, Cillian O'Sullivan (0-01), Brian O'Halloran; Jordan Morris, Mathew Costello (0-04, 0-03f), Eoghan Frayne (0-04, 0-02f).
Subs: Ruairi Kinsella for Ryan h/t, Cian McBride for O'Sullivan h/t, Ronan Jones (0-02) for Gray 49, James Conlon (0-02) for O'Halloran 55, Daithi McGowan for Hickey 62.
Referee: Joe McQuillan (Cavan).
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