In 1974, Alvi shot down the Israeli Air Force's Mirage III over the dogfight took place in Golan Heights in Syria, and was honored for his bravery with gallantry war-time medals by Syrian and Pakistan government.
Sattar Alvi was born in Bannu, NWFP, India in 1944, into a family that had the military background. His father was an officer in the British Indian Army who later served in the Pakistan Army. He was educated at the Bannu where he did his matriculation and attneded the Emerson College in Multan, Punjab where he secured his graduation.
In 1963, he was accepted to join the Air Force Academy in Risalpur where he received his flight training on the Cessna T-37T, and graduated in General Duty Pilot (GD) course in 1965. P/Off. Alvi participated in the second war with India in 1965, touring his duty as "Mail Runners" to convey messages from one base to another, served on this assignment until the war was ended.
From 1966–71, Flt.Lt (Capt.) Alvi was selected in the military advisor group for the Iraqi Air Force, where he qualified as a test pilot for the MiG-21 and sat up the training school for the Iraqi IAF. He returned to Pakistan to participate in the third war with India and flew the Quick Reaction Close Support Missions especially in Shakargarh, where the battle with the Indian IAF was the most turbulent. After the war in 1971, Flt.Lt Alvi was sent to join the faculty at the Air Force Academy and served as a flight instructor on the flight manuals on the F-7P, a Chinese variant of MiG-21F.
Pakistani prime minister Zulfikar Ali Bhutto sought to maintain close relationships with the Arab world. When the Yom Kippur war broke out, Alvi was one of the Pakistan Air Force fighter pilots who volunteered to go to the Middle East to support Egypt and Syria. By the time they arrived, however, Egypt and Israel had already concluded a ceasefire and only Syria remained in an active state of war against Israel. Alvi, who was serving as a Flight Lieutenant in 1973, joined the Syrian Air Force along with future-Air Chief Marshal of the Pakistan Air Force, Nur Khan. The PAF fighter pilots flew in a formation using the call-sign "Shahbaz" under Air Marshal Nur Khan.
On 26 April 1974, PAF fighter pilot Flight Lieutenant Sattar Alvi on deputation to No. 67A Squadron, Syrian Air Force (SAF) was flying a SAF MiG-21F-13 (Serial No. 1863) out of Dumayr Air Base, Syria in an eight-ship formation with a fellow PAF pilot and the Flight Leader, Squadron Leader Arif Manzoor.
Alvi came to worldwide international notice when he shot down the IAF's Mirage IIICJ flown by Captain M. Lutz. On 26 April 1974, while on an aerial patrol, the PAF fighter pilot team including, Flight Lieutenant Captain Sattar Alvi, Squadron Leader Major Saleem Metla and the formation's leader Squadron Leader Major Arif Manzoor had an encounter over the Golan Heights between a Mig-21 of the Syrian Air Force and two Israeli Mirages.
While leading a Mig-21 patrol along the border, Squadron Leader Arif Manzoor was apprised of the presence of two Israeli Phantom aircraft and was cautioned that these could be decoys while two other fast tracks approaching from the opposite direction might be the real threat. The latter turned out to be Mirages and a moment later Alvi, in Arif's formation saw the No 2 Mirage breaking towards him. All this time, heavy radio jamming by Israeli ground stations was making things difficult but the Pakistani pilots were used to such tactics. Sattar forced the Israeli pair into close combat, firing his K-13 missile at the first opportunity. The Israeli wingman's Mirage exploded into a ball of fire, while the leader quickly disengaged.
After the engagements, Flight Lieutenant Captain Sattar Alvi and Shahbaz formation leader Squadron Leader Major Arif Manzoor were awarded two of Syria's highest decorations for gallantry, the Wisaam Faris and Wisaam Shuja'at in 1973 by the President of Syria Hafez al-Assad in a public ceremony. The government of Pakistan also awarded each PAF pilot the Sitara-e-Jur'at. The prime minister Zulfikar Ali Bhutto personally met each of them and awarded the gallantry awards in public ceremonies.
After the war, Sattar Alvi was promoted to Wing Commander and went on to command PAF's elite Combat Commanders' School and the premier PAF Base Rafiqui. In 1994, he was promoted to Air Commodore (Brigadier) and commanded the Pakistan Aeronautical Complex (PAC) until 1998. He retired as an Air Commodore in 1998 and received an honourable discharge from the air force.