Replacements: Barry McNamara, Jason Cronin, Lee Nicholas, Hugh Kelliher, Dave Evans.
Replacements: Barry Elliott, John Dever, Alex Dunlop, Harrison Brewer, Shane Donovan.
An early Mark O'Neill penalty and a converted Ian Hanly try midway through the first half gave the visitors a 10-0 advantage at the interval.
They then raced into an unassailable 24-0 lead after Kyle McCoy and Mark O'Neill, who successfully kicked both conversions, went over after the restart.
James Murphy clawed five points back for Shannon late on, but Terenure College got the result they needed to secure a second league title win in two years.
"It's one of the best achievements of my career," said Terenure out-half Mark O'Neill on helping his team gain back-to-back promotions.
"The foundations have been built on hard work, strength in depth and implementing our game-plan in each match."
But despite wrapping up the league with three games to spare, O'Neill insists the job is not done.
"We put in a lot of hard work and it's paid off, but we still have three games left to play and we want to win at least two," he added.
The match on Saturday was played on the newly-opened Thomond Park back pitch and was competitive from the off.
Terenure survived a strong start from the home side as their disciplined defence kept Shannon out and prevented them from getting a foothold in the game.
After some excellent early attacking play by centre Ryan Roopnarinesingh, O'Neill opened the scoring with a well-struck penalty in the 11th minute.
From there the Leinster side went on to control possession and their dominance was rewarded when McCoy sent full-back Hanly over on 25 minutes.
Shortly after the restart, 'Nure effectively killed off the game with two converted tries inside 10 minutes.
The first came in the 44th minute following Graham Coffey's intercept and kick forward which ended with number 8 McCoy scoring in the corner.
'Nure's third try of the afternoon arrived six minutes later when Mark O'Neill took advantage of quick rucking from his pack to slide over to the left of the posts.
Shannon did get a deserved consolation score through a well-worked try from Murphy in the right corner on 71 minutes.
But the outcome, much like Terenure's progression to Division 1A, was never in doubt.
Referee: Kieran Barry (IRFU)