The result moved Estonia onto four points in League C Group 4 after three matches. Luxembourg remain on three points.
Peetson gives Estonia early lead
Estonia made the breakthrough just five minutes into the match when Rasmus Peetson found the net to put the hosts 1–0 ahead.
Luxembourg responded by seeing more of the ball, but Estonia remained organised and protected their advantage through the remainder of the contest.
Estonia hold firm
Luxembourg finished with 54 per cent possession, compared with Estonia's 46 per cent, but the hosts created the better chances according to the match statistics.
Estonia registered 14 shots to Luxembourg's eight and recorded an expected-goals figure of 1.49 compared with Luxembourg's 0.52.
Estonia successfully defended their early advantage to record their first victory of the current Nations League campaign.
Estonia's Group C4 position
The victory leaves Estonia with four points from three matches, following draws against Iceland and Bulgaria in their opening two games.
Their next Nations League fixture is another home match against Iceland on 6 October.
Scorers
• Estonia: Rasmus Peetson 5'
• Luxembourg: No goals