Replacements: Alex Simpson, Ed Rossiter, Conor Kindregan, Brian Walsh, Alan Rossiter.
Replacements: Adam Howard, Mark Cooney, Rob Cleere, Ben Woods, Gearoid McDonald.
The home side began nervously and were punished when they roamed offside after five minutes and winger Josh Glynn slotted the penalty.
Glynn doubled Old Belvedere's tally with his second penalty after 26 minutes but he missed a third as Andy Dunne's men failed to fully capitalise on their early dominance.
UL came to the boil approaching half-time with young out-half David Johnson going close to scoring the game's only try. Crucially for the hosts, their second row and captain Ed Kelly did manage to touch down shortly afterwards.
Following a series of drives, Kelly found a gap to drive over on the end of a maul and Ben Martin converted to have the hosts 7-6 in front.
Bohs pressed home their advantage in the scrum in the third quarter with props Tom Burke and Alex Simpson, who replaced the injured Gary Walsh, getting on top of their front row opponents.
Full-back Martin rewarded their consistent scrummaging by landing a 45th minute penalty, but he missed a further kickable effort and Glynn was soon on target again to leave only a point between the sides.
After Glynn failed with a fourth attempt on goal, UL built through the phases and a second successful penalty from Martin in the 77th minute proved to be the match-winning score.
Colm Tucker jnr's side had to dig deep in the dying minutes as their defence just about held 'Belvo at bay, handing the Dublin 4 club their fifth straight defeat.
Credit to Dunne's charges though, they threw everything at the hosts with flanker Michael Oyuga just held up short and scrum half David Moore steering the pack close to the try-line on a couple of occasions.
Bohs remain second-from-bottom, but their fourth victory of the league campaign means there are only two points between themselves and eighth-placed 'Belvo.
Tucker told the Limerick Leader afterwards: "A welcome and important victory. We have a young team, particularly at 9, 10 and 12 and the experience of winning will be of benefit to them.
"Our front row did well despite losing Gary Walsh early on and it was close at the end but we'll take these four points. Next Friday is another big challenge for us when we go to Dooradoyle to take on Garryowen."
Referee: Eddie Hogan O'Connell (IRFU)