Monaghan held firm in tense circumstances late on at Croke Park to record their first ever win at the All-Ireland quarter-final stage.
The Ulster county had lost all five of their previous quarter-final games but edged out Kildare in an arm-wrestle encounter to ignite their Super 8s challenge.
The sides were level with five minutes of normal time remaining but Monaghan points from Vinny Corey, Conor McManus and Rory Beggan ultimately sealed the crucial win.
It sets Monaghan up nicely for next Sunday's glamour home game in Clones when Kerry will be the visitors.
As for Kildare, it's their 11th loss in 12 league and Championship encounters at Croke Park and they will feel they simply have to beat Galway in Newbridge next Sunday to keep their All-Ireland semi-final hopes alive.
The form lines beforehand were similar for both sides who gained redemption through the qualifiers after surprise provincial championship defeats.
Kildare lost out to Carlow in Leinster though pulled off four big wins in the qualifiers over Derry, Longford, Mayo and Fermanagh last weekend.
They got the better start here too with a sixth minute Daniel Flynn goal putting them 1-01 to 0-02 ahead.
The former Aussie Rules professional showed real determination to hit the net as Keith Cribbin was unmarked on his right but Flynn powered on himself before firing home.
The score should have kick-started Kildare but they only added another two points from open play in the half.
Rather it was Monaghan who grabbed the impetus and finished the half with 10 points to their credit.
Karl O'Connell booted over two of those having curled over two beauties against Laois in Navan.
McManus helped himself to three points also as Monaghan sought to repeat their qualifier win of 2014 over the Lilies.
Monaghan led 0-10 to 1-05 at the break though had goalkeeper Beggan to thank for a fine save to deny Flynn a second goal in the 16th minute.
O'Connell added a third point in the 49th minute but it was Monaghan's only score between the 31st and 57th minutes minutes.
Kildare weren't exactly prolific in the meantime but they did twice bring the game back to level terms with points from Fergal Conway, Neil Flynn and Johnny Byrne.
They were deadlocked for a third time at 1-9 to 0-12 with 65 minutes played when Vinny Corey put Monaghan ahead with a fine point from distance.
It was a lead that Monaghan would this time retain and McManus doubled their advantage with an excellent point in the 70th minute.
Kildare sub Eamonn Callaghan cut the gap to the minimum again but a 75th minute Beggan point from a free proved the insurance score for Monaghan.
Monaghan: Rory Beggan (0-02, 0-01 45, 0-01f); Ryan Wylie, Drew Wylie, Kieran Duffy (0-01); Fintan Kelly, Vinny Corey (0-01), Dessie Mone; Niall Kearns (0-01), Darren Hughes; Ryan McAnespie, Shane Carey (0-01), Karl O'Connell (0-03); Conor McCarthy (0-02), Conor McManus (0-04, 0-01f), Owen Duffy.
Subs: Paudie McKenna for Duffy, black card (17), Jack McCarron for Kelly (48), Kieran Hughes for McKenna (60), Dermot Malone for Carey (66).
Kildare: Mark Donnellan; Mick O'Grady, David Hyland, Peter Kelly; Johnny Byrne (0-01), Eoin Doyle, Kevin Flynn; Kevin Feely (0-01, 0-01f), Tommy Moolick (0-01); Fergal Conway (0-01), Paul Cribbin, Keith Cribbin; Paddy Brophy, Daniel Flynn (1-01), Neil Flynn (0-04, 0-02f).
Subs: Niall Kelly for Paul Cribbin (46), Chris Healy for Brophy (50), David Slattery for K Cribbin (58), Eamonn Callaghan (0-01) for Moolick (69), Cathal McNally for N Flynn (71).
Referee: A Nolan (Wicklow).