Mosquito eggs and larve in houseplant soil & water?

I have a large palm which summers outside after frost and winters inside. I have noticed mosquitos in my house. Upon further investigation I have found that the water that runs into the tub which holds the plant has larve which are hatching. Is there anything I can add to the soil or water which has run out the bottom that would kill the larve without harming the tree or a threat to us and our dogs. Eventually the water dries up, but until then I am stuck with this problem. I guess the mosquitos from summer laid eggs in the soil. We thought we had the hole in the bottom on the container sealed, but water runs out anyway. Using a shop vac to vacuum out the water is a whole lot of trouble. This is a ceiling high palm. Any suggestions?