Laois forward Eoin Lowry was the star forward for the 2016 champions, and he scored 1-7 while Jack Barry landed the other goal, after UCD led by 1-8 to 0-1 at half-time in Maynooth.
The hosts had Tom Hannifan and Jason Gibbons shown black cards after half-time, and they had already kicked 10 wides in the first-half, with Keith Beirne’s second-half penalty a mere consolation.
“We were very nervous coming out here because we hadn’t any competitive football since November 30,” said Divilly.
“We had one challenge game after Christmas and that’s it because of O’Byrne Cup involvement and our guys only came back to college yesterday.
“It was a bit of a shot in the dark how things were going to go today. But in fairness to the guys they are a good bunch.
“They went out and played what they had in front of them.”
Dublin All-Ireland winner Con O’Callaghan was rested by Divilly but UCD still had plenty of star quality and raced into a 1-5 to 0-0 lead after 16 minutes.
Eoin Lowry scored 1-2 and the goal arrived when he burst in from the left before he finished past Maynooth goalkeeper Niall Carrie.
The Kildare outfit were poor in front of goal in the first-half and captain Ryan O’Rourke scored their only point in the 17th minute.
He added two more after the interval but UCD were brilliant and Kerry youngster Barry lobbed Carrie to put the result beyond doubt just three minutes after half-time.
“In the first-half we got 13 shots off, the same as UCD, they kicked 1-8 and we kicked a point,” said Maynooth boss John Doyle.
“You can come up with all the training and the gym but it’s about kicking the ball over the bar.”
E Lowry 1-7 (0-5f), C McCarthy 0-3 (0-2f), J Barry 1-0, L Casey 0-3, E O’Carroll 0-1, J Feehan 0-1.
K Beirne 1-2 (1-0 pen), R O’Rourke 0-3 (0-1f), K O’Callaghan 0-1.
C Manton (Tipperary); L Fortune (Cavan), C O’Shea (Dublin), C Mullaly (Dublin); E Murchan (Dublin), S Coen (Mayo), J Feehan (Tipperary); B O’Sullivan (Kerry), J Barry (Kerry); L Casey (Tipperary), C McCarthy (Monaghan), P O’Connor (Sligo); B Byrne (Kildare), E O’Carroll (Laois), E Lowry (Laois).
T Hayes (Cavan) for O’Connor (30), L Moran O’Carroll (52), B O Seanachain for Casey (52), J Rossiter for Lowry (59), D Maguire for O’Sullivan (59).
N Currie (Louth); J Gibbons (Kildare), M Hyland (Kildare), J Mooney (Meath); E O’Donnell (Donegal), T Hannifan (Dublin), C Cannon (Donegal); P Cribbin (Kildare), P Brophy (Kildare); D O’Baoill (Donegal), R O’Bourke (Leitrim), D Flynn (Kildare); A Jones (Monaghan), P Fogarty (Kildare), K Beirne (Leitrim).
K O’Callaghan (Kildare) for Cannon (30), L Knowles (Laois) for Hannifan (33, black card), C Dunne (Westmeath) for Jones (37), S McDonagh (Donegal) for Gibbons (55, black card).
Martin McNally (Monaghan).