Eynesbury had to settle for a point in their first Spartan South Midlands League match for 80 years.
Rovers were held to a 1-1 draw by Oxhey Jets in their Premier Division season-opener at Hall Road last Saturday.
The local club made a sideways switch from the United Counties League - their home since 1963 - during the summer and began impressively as debutant Craig Daniel fired them ahead in the 18th minute.
But Rovers were left to rue their failure to take a number of other excellent chances when being pegged back with 20 minutes to go.
"We didn't play brilliantly by any means, but we still carved out more than enough chances to win the game comfortably," said Eynesbury assistant boss Warren Brown.
"We started off brightly and deserved to be ahead, but we couldn't get the second goal that would have killed the game off.
"We missed a lot of easy chances and it felt more like a defeat than a draw in all honesty.
You may also want to watch:
"We've got to be more clinical in the final third."
Rovers were close to an opener in the first minute as Dan Draper fired over the bar but Daniel did soon provide a spectacular breakthrough with a 25-yard blast.
Jack Uttridge preserved Rovers' advantage with a goal-line clearance just before half-time when defensive stalwart James Ducket's 300th appearance in Rovers' colours was brought to an end by an ankle injury.
New recruit Jake Stronge was sent on in his place and almost made a grand entrance when hitting the underside of the bar within seconds of his introduction before fellow former Newport Pagnell man, Dave Baker, headed wide from a good position.
But Rovers were stung when Carlos Simao levelled for Jets and they couldn't respond with a winner despite the visitors having a player sin-binned late on.
Danny Draper came closest to restoring the advantage when heading an Uttridge cross inches wide in stoppage time.
Eynesbury now go to Biggleswade United tonight (Tuesday) before hosting former United Counties League rivals Wellingborough Town in the extra preliminary round of the FA Cup this Saturday, 3pm.