It took a penalty by captain Barry Quinn to spark only the second win in eight matches under manager Don Givens for the Republic of Ireland Under-21 side.
But only dogged Estonian defending on a drenched pitch prevented them running up a big score in this European Championship qualifier.
Almost from first whistle to last, the Irish had complete control of a one-sided match against low-grade opposition who could only raise four substitutes to sit on the bench.
A drenched 3,000-plus crowd in Buckley Park, Kilkenny, willed local hero Michael Reddy, the striker they sold to Sunderland for £35,000 two years ago, to register a goal on his emotional return in the green shirt.
But they had to settle for him engineering the 57th-minute spot-kick which decided the match.
Reddy, all pace and determination, dashed into Estonia's heavily-populated box 12 minutes after the break and was brought down by right-back Taavi Rahn for as clear a penalty as you could wish to see.
Given an earlier miss of almost monstrous proportions, the choice of Quinn to take it may not have looked too wise but the tireless Coventry midfielder made no bones about converting it in confident style.
There should have been far more goals for the Irish but on this rainy, miserable night, just keeping your feet and your balance was a work of art.
In the end their willingness to keep passing the ball rather than lump it hopefully at a heroic Estonian rearguard paid off and that will have pleased boss Givens most.
Although goalkeeper Joe Murphy had to make a save in the first minute from Aleksander Saharov's header and then striker Joel Lindpere shot inches wide following a free-kick 13 minutes later, the Republic youngsters soon established total first-half command.
Estonia were content just to absorb a narrow defeat and for Ireland, whose lead was never seriously threatened, it was just a case of seeing the job through.
Republic Of Ireland: J Murphy, Healy, Gavin, O'Shea, Clarke, B Quinn, J O'Connor, D Lynch, Barrett, Reddy, Doherty. Subs: Partridge, McGrath, Hunt, Miller, Rowlands, D Delaney, Byrne.
Estonia: Kisseljov, T. Rahn, Parnpuv, Vink, Cash, Zahhoviako, M. Kosemets, Sahorov, Lindpere, Kirillov, Tikenberg. Subs: K Kutt, M Kahr, Maasing, Jaager.
Referee: S Kandare (Slovenia)
