The hosts went into the game on the back of three consecutive defeats and will have been looking to find form ahead of their AFC Asian Cup qualifier with Syria next Tuesday.
And they made the perfect start as Amri turned home Hafiz Abu Sujad's cross to give Bernd Stange's men the lead after just one minute at the Jalan Besar Stadium.
Singapore continued to offer the more potent attacking threat as they went in search of a second, while their visitors struggled to muster any chances of note.
Amri tested the Laos defence throughout, the striker going close on three occasions as Singapore sought to take a commanding lead.
Laos' only promising moments came on the counter-attack, but it was Singapore who created the better openings, goalkeeper Seng Athit Somvang keeping the deficit at one with a fine save from defender Shaiful Esah midway through the second half.
The away side were never really able to gain a foothold in the game and they were fortunate not to fall further behind in the closing stages.
Shahdan Sulaiman and Sahil Suhaimi both wasted late opportunities and midfielder Shahril Ishak struck the post, but one goal proved to be enough for the dominant hosts.
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