Two goals in five minutes at Khalifa Stadium set Bruno Metsu's side on its way. Bilal Mohammed planted a far-post header into the bottom corner in the 11th before Mohamed El Sayed took advantage of a goalmouth scramble to curl in the second in the 16th.
Substitute Fabio Cesar wrapped up the victory in the 86th by curling a left-foot freekick around the wall and into the top corner past a static goalkeeper.
The hosts go through in second place behind group winner Uzbekistan, which drew 2-2 with China in the other game.
Many of the 28,339 crowd had left Khalifa Stadium before the final whistle, but that may have been the result of such an easy win.
Kuwait had beaten Qatar on its way to winning November's Gulf Cup, but it never threatened to repeat that triumph at the Asian Cup and leaves the tournament without a point.
Despite its losses to China and Uzbekistan, Goran Tufegdzic's team still had an outside chance of progressing to the quarterfinals if it won its final group game.
Qatar, which lost to Uzbekistan in its opener but then beat China 2-0, all but ended those hopes with a dominant first half display.
Top scorer Sebastian Suria, a constant threat throughout, should have scored his first goal of the tournament in the first minute but headed over, and Lawrence's driven free kick was tipped over by goalkeeper Nawaf al-Khaldi moments before the opening goal.
Bilal settled any nerves when he powered in a header from Ibrahim al-Ghanim's deep cross, and the second goal sparked a Mexican wave.
El Sayed appeared to push his marker out of the way in order to reach a long ball out of defense, but no whistle came, and though his header was saved and Suria's follow-up was blocked, El Sayed eventually picked up the loose ball and curled it into the top corner, with al-Khaldi out of his goal.
Kuwait's best chance came right at the end of the half when a cross from the right found Walied Ali in space at the far post, but his angled shot was diverted behind by keeper Qasem Burhan.
Qatar sat back on its lead after the break but, despite plenty of possession, Kuwait couldn't take advantage and gradually ran out of steam.
Cesar, a 73rd-minute replacement for Yousef Ahmed, put the seal on the win with a perfectly-placed free kick which keeper al-Khaldi did not even move for.