The hosts dominated for long periods of the game and had out-half Noel Reid to thank for some assured place-kicking as he added two penalties to two conversions.
Connacht scrum half Adam Kennedy replied with four penalties, which kept the visitors within touch.
However, skipper Jack O'Connell led from the front in an excellent forward effort and Richie Murphy's side were good value for their win.
LEINSTER U-20: A Conway; C Lilly, B Macken, D Lynch, D Hudson; N Reid, J Cooney; J O'Connell, R Byrne, M Moore (A Lyons 66), R Lennon, B Marshall, C O'Brien (R Ruddock 50), J Murphy, R Bent
CONNACHT U-20: P Finn; T O'Halloran, E Griffin, F Gormley, C Conroy; C Murphy (M Dolan 66), A Kennedy; D Buckley, K Egan, J Robinson, S Casey, C Raftery (R Keirns 60), A Spring, R Cunningham, A Spring, S Conneely
Referee: Trevor Collins (IRFU)