To determine the correct words to fill the blanks, we need to understand the difference between the homophones "complement" and "compliment":

1. Complement (verb/noun): To complement means to contribute extra features to someone or something in such a way as to improve or emphasize their qualities; to go well with or complete something else.
In the context of the first blank, "The dress complemented her so well..." means that the dress suited her, enhanced her look, or went well with her appearance.

2. Compliment (verb/noun): To compliment means to politely congratulate or express praise, admiration, or approval to someone.
In the context of the second blank, "...they all immediately complimented her on her appearance" means they praised her or said nice things about how she looked.

Therefore, the first blank requires "complemented" and the second blank requires "complimented".

Thus, the correct pair of words is complemented, complimented.