Water the tomato plant in its container until the water comes out of the drainage holes in the bottom of the pot. This will help soil stick to the root ball, which will prevent them from becoming too dry during the transplanting process.
Fill the larger pot one-third of the way with the same potting mix you used in the original container. Pry the tomato out of the original pot by inserting a butter knife between the soil and the sides of the pot.
Pull the tomato out of the old pot by its leaves, not its stem. Lower the tomato into the larger pot. Backfill the pot with the soil so the lowest set of leaves is just above the top edge of the new pot.
Fill the new pot the rest of the way with soil, bringing the soil level up to just under the lowest set of leaves. The buried stem will root.
Water until the water comes out of the drainage holes. Apply a liquid fertilizer to the soil once a week according to the package directions.
Keep the plant out of direct sun for two days. Move the plant to full sun after the two days are over.