From this blog followed by an answer, I have found Lord Shiva to destroy three cities with just a smile - all that set up was extraneous. Which literature or scripture talks about that? The answer or blog says the story belongs to a tamil literature. As a possibility, it might be one of the poem of a Nayanar also.
The destruction of Tripura by Lord Shiva is an event described in Vedas as I discuss here so, it's possible that there are many variants of this story on taking account the cyclical nature of creation. And event described in Linga Purana states that Lord Shiva destroyed Tripura with his look before shooting arrow.
किं रथेन ध्वजेनेश तव दग्धुं पुरत्रयम्।।
इषुणा भूतसंघैश्च विष्णुना च मया प्रभो।।
पुष्ययोगे त्वनुप्राप्ते पुरं दग्धुमिहार्हसि।।
यावन्न यांति देवेश वियोगं तावदेव तु।।
दग्धुमर्हसि शीघ्रं त्वं त्रीण्येतानि पुराणि वै।।
अथ देवो महादेवः सर्वज्ञस्तदवैक्षत।।
पुरत्रयं विरूपाक्षस्तत्क्षणाद्भस्म वै कृतम्।।
सोमश्च भगवान्विष्णुः कालाग्निर्वायुरेव च।।
शरे व्यवस्थिताः सर्वे देवमूचुः प्रणम्य तम्।।
दग्धमप्यथ देवेश वीक्षणेन पुरत्रयम्।।
अस्मद्धितार्थं देवेश शरं मोक्तुमिहार्हसि।।
अथ संमृज्य धनुपो ज्यां हसन् त्रिपुरार्दनः।।
मुमोच बाणं विप्रेंद्रा व्याकृष्याकर्णमीश्वरः।।
तत्क्षणात्त्रिपुरं दग्ध्वा त्रिपुरांतकरः शरः।।
देवदेवं समासाद्य नमस्कृत्वा व्यवस्थितः।।
रेजे पुरत्रयं दग्धं दैत्यकोटिशतैर्वृतम्।।
इषुणा तेन कल्पांते रुद्रेणेव जगत्त्रयम्।।
ये पूजयंति तत्रापि दैत्या रुद्रं सबांधवाः।। (Linga Purana Purva Bhaga Chapter 72)
O Is’a, O lord, what is the use of burning Tripura with the chariot, flag, arrow, Brahma or myself or the bhutas? The Pusyayoga has arrived. Before the three cities get separated, you reduce them to ashes, by that time." Then Virupaksa - Mahadeva, the omniscient one, reduced Tripura to ashes. Then all the gods like the moon, Visnu, Kalagni and the wind god, collectively offered their salutation to lord Siva and said to him— “O Deves’a, with your mere look, Tripura has been reduced to ashes; still for the welfare of the world, you should shoot the arrow. Thereafter, O leading Brahmanas, Tripurari lsvara lifted the bow and stretching its string upto the ear, smilingly shot the arrow. The Tripuras were burnt in a moment by the arrow and returned to the lord. It offered its salutation to lord Siva and stood besides him. Tripura was filled with bodies of the hundreds and thousands of dead daityas. At the end of the kalpa, Tripura resembled the three Iokas which were reduced to ashes. However, in Tripura itself, such of the Daityas who were devoted to Siva, they together with their kins and families achieved the abode of Siva on the basis of their devotion.