Combine first 6 ingredients, 1/4 teaspoon salt, and 1/8 teaspoon pepper in a food processor; process until smooth, scraping sides of bowl occasionally. Gradually add oil through food chute with food processor on; process until smooth.
Cook pastas according to package directions, omitting salt and fat. Drain in a colander over a bowl, reserving 3/4 cup cooking liquid. Combine pastas, pesto mixture, tomatoes, reserved cooking liquid, remaining 1/2 teaspoon salt, and remaining 1/8 teaspoon pepper in a large bowl; toss well.