Linga Purana (chapter 64) states worship of Lord Shiva done by Parashara using various Vedic Suktas which I also mention in my answer here. The verses are as:
अदृश्यंति वशिष्ठं च प्रणम्यारुन्धतीं तत । कृत्वैकलिंगं क्षणिकं पांसुना मुनिसन्निधौ ।। संपूज्य शिवसूक्तेन त्र्यंबकेन शुभेन च। जप्त्वा त्वरितरुद्रं च शिवसंकल्पमेव च।। नीलरुद्रं च शाक्तेयस्तथा रुद्रं च शोभनम्। वामीयं पवमानं च पंचब्रह्म तथैव च।। होतारं लिंगसूक्तं च अथर्वशिर एव च। अष्टांगमर्घ्यं रुद्राय दत्वाभ्यर्च्य यथाविधि।। (Linga Purana chapter 64)
Then Parashara bowed in reverence to Adryasanti - his mother, Vasistha and Arundhati - his grandparents. In presence of the sage Vasistha, he made a temporary Linga of clay. Then he reciting the hymns from the Shiva Sukta, Tryambakam mantra, Tvarita Rudra, Siva Sankalpa, Nila Rudram, Shakteya- Rudra, Vamiya, Pavaman Sukta, PanchaBrahman Sukta, Linga-Sukta and Atharvasiras mantras, adored the Shivalinga. After worshipping the linga appropriately, he offered Ashtangya Arghya to Rudra.
Most of the hymns here I can recognize; For example the Tryambakam mantra is found in Rig, Yajur and Atharva Veda. Shiva Sankalpa Sukta is found in Yajurveda as well as Rigveda khilani. Vamiya and Pavaman suktas are found in Rigveda. The PanchaBrahman and Linga Sukta are found in Taittariya Aranyaka. Atharvasiras and Nila Rudra are upanishads. I do not know of Shakteya hymn though.
I'm interested to know more about about the Tvarita Rudram. Where is it found? It is likely that it should be found in Vedas as all other Suktas above are also found in the Vedas. Also the Twarita Rudram seems to be widely used in Lord Shiva worship as the Shiva Purana also mentions about it. Shiva Purana Vyayaviya Samhita chapter 24 in the chapter 'Rituals to worship Shiva' also mentions:
पवमानेन रुद्रेण नीलेन त्वरितेन च | लिंगसूक्तादिसूक्तैश्च शिरसाथर्वणेन च || ४७ || ऋग्भिश्च सामभिः शैवैर्ब्रह्मभिश्चापि पञ्चभिः | स्नापयेद्देवदेवेशं शिवेन प्रणवेन च || ४८ ||
The hymns of Pavamana, Rudra, Nila and Tvarita or the hymns of Linga Sukta or the hymns from Atharvasiras Upanisad or the hymns from the Rigveda or Samaveda relating to Siva or the five Brahmans be used for the ablution of the lord of the chiefs of the gods. The name Siva and the Pranava too shall be used.
By the name of Tvarita it is likely that it is used to give quick results or it could be also about specific form of Lord Rudra as Tvarita Rudra. Is this Tvarita Rudra Sukta still available or it is already lost? If it is possible please post the Suktas also.