Shevchyk scored the next two goals, with his second being the 500th scored in Paralympic history.
Gold medal contenders Russia and Ukraine claimed confident, high scoring victories in the first day of football 7-a-side action.
Ukraine showed the Riverbank Arena why they are the number one side in the world with a dominant 9-0 victory over USA.
Anatolii Shevchyk grabbed four of the goals and scored a milestone 500th goal in Paralympic history.
It only took 60 seconds for Ukraine to score the first goal of the game when Ivan Shkvarlo converted Ivan Dotsenko’s low cross.
Dotsenko and Vitaliy Trushev added two more to make the score 3-0 in under 10 minutes.
Shevchyk scored the next two goals with his second being the 500th scored in Paralympic history.
Shevchyk took his tally to four goals after the break in addition to further efforts from Shkvarlo and Taras Dutko to complete the comprehensive victory.
Their Russian rivals made light work of opponents Argentina. Aleksandr Kuligin, Andrei Kuvaev and World Championship MVP Lasha Murvanadze bagged two goals each in a convincing 8-0 victory.
It was one way traffic in the first half as Russia raced into a 3-0 lead at halftime. Kuligin opened the scoring from a free kick as he drove the ball into the top right hand corner.
Murvanadze doubled the advantage by tapping in from close range and then claimed his second moments later, weaving through the Argentine defence and finishing confidently.
The floodgates opened in the second half with Eduard Romanov smashing the ball into the back of the net to make it 4-0.
Kuligin and substitute Kuaev added two more to the scoreboard. Kuavev nodded in a cross from midfielder Viacheslav Larinov to round off a strong start to the tournament for the world champions.
Beijing bronze medalists Iran kick started their tournament with a comfortable 4-1 win over the Netherlands, after going 3-0 up after the first 30 minutes.
Iran took the lead in the fourth minute with Farzad Mehri hitting the target from a free kick on the edge of the 12-yard box.
The prolific Moslem Akbari could have made it 2-0 but he stroked the ball inches past the post.
Akbari didn’t have to wait long to collect his first goal of the tournament, though, as he buried a shot low into the corner with three minutes until the break.
Abdolreza Karimizadeh scored Iran’s third goal when he found a gap underneath goalkeeper George van Altena to make it 3-0 at half time.
Dennis Straatman netted a consolation for the Dutch before Iran’s Bahman Ansari finalised the scores with his fine finish.
Brazil ended the day’s competition with a comfortable 3-0 result against hosts Great Britain in front of an energetic sold out home crowd at the Riverbank Arena.
Almeida de Souza opened the scoring with a low shot that was beyond goalkeeper Billy Thompson’s reach with 10 minutes gone on the clock.
Wanderson Silva extended the lead firing a shot into the roof of the net moments later.
Yurig Ribeiro dos Santos scored Brazil’s third with a sensational free kick effort that flew across goal into the top corner.
The roars of the home support motivated Great Britain in the second half, but despite creating a few chances, they were unable to get on the scoreboard.