If the Robins beat Mansfield Town at home and MK Dons lose at Stockport County next week, then they are promoted with two more games to play.
Otherwise it will definitely take four more points to do the trick after substitute striker Jutkiewicz notched an 85th-minute winner against the Shakers.
The 18-year-old, who has signed a pre-contract agreement with Everton for next season, came on at half-time for Barry Corr.
It had looked for most of the game like a certain goalless draw which would have been a fair reflection because for the first half, certainly, there wasn't an ounce of quality on show.
It was only because both teams realised the game was there for the taking, that the tempo increased in the second half.
Blair Sturrock missed three chances for the Robins, while Dave Challinor, Glynn Hurst, Andy Bishop and Jason Kennedy did the same for the hosts.
But Jutkiewicz made sure that it wasn't going to finish goalless when he latched on to a right-wing Aaron Brown corner that had been headed back across goal.
Shakers keeper Andy Warrington came up for a last-minute corner and headed against the post.
And in some ways that incident summed up Bury's luck at present. They now are only three points clear of the relegation places with three games to play.