Boylan stated that his players were 'very well' prepared mentally after the manner of their Leinster semi-final defeat seven days earlier and praised them for taking on the responsibility themselves.
The essential difference between the two performances was that Meath had the cushion of a 12 point lead before the home side powered their way back into contention.
And, they also had Nigel Crawford back after injury, playing a major role in boosting midfield and having a key influence on the outcome.
The two managers were in general agreement that Meath were fortunate enough to hold out for an admittedly deserved win after adding a mere two points to their interval total of 2-8.
Boylan conceded that it had been 'a battle' with the clock running out when Monaghan reduced the margin to four points in injury time.
"We got the scores at the right time and we got the breaks at the right time," he said.
"I suppose we really don't know where we are but we're still in the All-Ireland series and we're very thankful for that."
For his part, Monaghan manager Colm Coyle (who made his championship debut for Meath, in 1983, on Boylan's first day in charge), felt that 'anything could have happened' if they had maximised their chances in a second half that saw them add ten points to an embarrassing two achieved by the break.
Against Kildare Meath opened smartly, to lead 1-3 to 0-1 after 12 minutes, before losing their way.
This time, they also gained the boost of an early (Graham Geraghty) goal, but enhanced their position through more economic play and stronger finishing.
In general, form in the county's first championship match outside of Leinster, represented a significant improvement on the previous week, with all of their experienced campaigners contributing hugely.
Eoin Lennon started well at midfield for Monaghan but once Nigel Crawford settled down Meath quickly established a grip aided by the wind.
After 18 minutes, Meath led 1-5 to 0-1 and were not being seriously troubled because of obvious difficulties Monaghan had in building attacks through determined play at the back.
Disappointingly for them, top scorer Paul Finlay was not involved until later in the half and, overall, the outlook didn't look promising.
"We were at sea. Meath were dominant in practically every position and physically, they were stronger and playing in a different gear," added Coyle. "We were just hanging on."
A second goal, from David Crimmins in the 35th minute, was followed by a quick point from the hard-working Giles.
It saw Meath go in at half-time 2-8 to 0-2 in front, with the home players feeling rather frustrated.
Coyle who remarked later that it had been 'a killer' to concede a goal and a point at the end of the half suggested that this was the difference at the end.
"We knew the wind was coming. I just said to the lads to go out and show a bit of pride and I think they answered it. We missed a lot of frees, but having said that, Meath were the better team overall."
Meath almost had another goal on the resumption when wing-back Anthony Rooney denied John Cullinane.
That was in the 39th minute. And, while Monaghan saw goalkeeper Cormac Sullivan save from Thomas Freeman a minute later, the home side were to settle down to force the pace of the game over the last quarter.
By now, Rory Woods was proving quite effective at centre-forward, while Kieran Tavey another substitute was to justify his introduction on the left wing.
For a long time, however, progress was slow because of the dominance of the Meath full-back line, with team captain Darren Fay at his best, but gradually the pressure began to tell with Finlay now contributing significantly.
In contrast, Meath were limited to a Cullinane point in the 49th minute and just one more from able substitute Evan Kelly seven minutes from time.
Boylan said afterwards that he wasn't sure if had been caused by tiredness or Monaghan's tenacity, but, one way or another he admitted that he wasn't happy until the final whistle went.
*Whatever Meath might have felt about Michael Collins' refereeing of previous games, they could have no complaint this time. He was typically efficient.
Scorers for Meath: D. Crimmins 1-2; G. Geraghty 1-1; T. Giles and S. McKeigue 0-2 each; D. Regan (free), E. Kelly and J. Cullinane 0-1 each.
Monaghan: R. Woods 0-6 (0-3 frees); P. Finlay 0-4 (0-2 frees, 0-1 fifty); T. Freeman and K. Tavey 0-1 each.
MEATH: C. Sullivan; N. McKeigue, D. Fay (capt.), C. Murphy; P. Reynolds, H. Traynor, N. Nestor; N. Crawford, C. McCarthy; T. Giles, J. Cullinane, G. Geraghty; D. Regan, D. Crimmins, S. McKeigue.
Subs: E. Kelly for Regan (injured, 36th minute); R. Kealy for Crimmins (second half); O. Murphy for S. McKeigue (63rd); A. Moyles for McCarthy (68th); M. O'Reilly for Reynolds (70th).
MONAGHAN: G. Murphy; J.P. Mone, D. McKenna, P. McKenna; D. Duffy (capt.), J. Coyle, A. Rooney; E. Lennon, J. Hughes; N. Corrigan, M. Slowey, D. McArdle; P. Finlay, R. Ronaghan, T. Freeman.
Subs: R. Woods for Slowey (25th minute); K. Tavey for Corrigan (second half); F. Markey for Hughes (56th);D. Larkin for McArdle (59th).
Referee: M. Collins (Cork).