She pulled the door open.

Literal

She [topic-は] door [object-を] pulled [then-て] opened.

引いて開けた chains two verbs with the te-form, but here the relationship is closer to manner-and-result than pure sequence: 'opened (it) by pulling.' Japanese has push-vs-pull as a recurring observation — 押す ('push') and 引く ('pull') label door behaviors and appear on signs (押す for push doors, 引く for pull doors) all over the country. The construction here doubles up the manner with the action to make the means explicit, where a single verb 開けた wouldn't say how.