Pembroke wicket-keeper batsman Tucker struck nine boundaries in his 107 ball innings, sharing a sixth wicket partnership of exactly 100 with Strabane's Aaron Gillespie (47) after Ireland had been on a precarious 97 for 5 against the African side.
Batting first, Sonny Cott had been run out without facing a ball, while the in-form skipper Jack Tector (13) gave Waiswa a return catch to leave a nervous Ireland 17 for 2.
A third wicket stand of 57 between Gary McCintock (33) and Adam Dennison (30) brought stability to the innings, before they and William McClintock (5) all departed in quick succession.
Tucker's innings saw him become the leading run scorer in the competition (131) and allowed Ireland to finish on 255 for 8, and that proved way beyond the reach of Uganda.
Rory Anders continued his impressive tournament with the ball - his 4 for 29 taking his tally to 10 - the leading bowler in the event to date.
Merrion left-armer Tom Stanton took 3 for 20, while the other successful bowlers were Josh Little (1-20) and Ben White (1-25) as Uganda were dismissed for 97.
There was one moment of drama in the Uganda innings as Kenneth Waiswa was dismissed first ball as he was given out for handling the ball by umpires Sarika Prasad and Ian Thomson.
The result keeps Ireland in second place behind Nepal on NRR - the Nepalese were comfortable six wicket winners over USA.
Both teams are now guaranteed of their places in Thursday's final which will decide who takes the last qualification slot for the U19 World Cup finals in Bangladesh next year.
The teams will meet before then in a dress rehearsal on Wednesday to decide who tops the group.
U19 World Cup Qualifiers
At Royal Selengor Club,
IRELAND U19'S 255/8 (50 overs, L Tucker 90, A Gillespie 47, G McClintock 33, A Dennison 30, D Wabwire 2-53)
UGANDA U19'S 97 all out (23.5 overs, A Lubega 26, R Anders 4-29, T Stanton 3-20)
Ireland U19's beat Uganda U19's by 158 runs.