This is the 10337th most frequent Japanese word.
駆け付ける
"To rush or hurry to someone's aid or to a location."
駆け付けた is used to describe the urgent movement of the firefighters toward a location (the house with the fire) to provide assistance or deal with the situation.
消防士たちは、火事が起きた家に急いで駆け付けた。
The firefighters rushed to the house where the fire occurred.
駆け付ける is used here to indicate hastening to attend the party or being present for the event out of a sense of commitment or enthusiasm.
友人の誕生日パーティーに駆け付けるために、彼は早めに仕事を切り上げた。
He finished work early to hurry to his friend's birthday party.
駆け付けて specifies the action of promptly moving to a location in response to a problem or need.