Fill a large pot with lightly salted water and bring to a rolling boil; stir in tortellini. Cook uncovered, stirring occasionally, until the tortellini are tender, about 12 minutes. Drain.
Heat olive oil in large skillet over medium heat. Add chicken; season with parsley, lemon juice, chili powder, salt, and black pepper. Cook and stir until chicken is no longer pink and the juices run clear, about 5 minutes.
Stir mushrooms, spinach, and kale into the skillet; cook until wilted, about 5 minutes. Reduce heat slightly and add tomato and pesto; cook and stir until flavors combine, about 5 minutes. Serve over tortellini.
