The Rabobank rider held off the GreenEdge man in a thrilling climax to the 132km stage from Fethiye to Marmaris to secure the ninth victory of his career.
So close were the riders as they went over the line that it needed a photo to confirm Renshaw as the winner, while Italy's Daniele Colli (Type 1 Sanofi) was third.
With the field bunched up the general classification was unchanged by the day's racing, with Bulgaria's Ivailo Gabrovski retaining the one minute 33 second advantage he earned with his heroic victory on stage three.
"I've been chasing this for several weeks. I worked very hard to get a victory and its great to finally get it with such a great field," said Renshaw.
"After the last corner, I knew I needed to hit the front early to beat Matt Goss. We're both pretty fast and at roughly the same speed. It was down to the one who jumped first. The line came quick enough for myself."
Renshaw added that he was honoured to lead an Australian one-two on ANZAC day.
"Today is a very special day in Australia and it's a very special day for me to win as ANZAC days honours all the sufferings of the Autralians. I'm very proud to win today for Australia," he said.
Goss was positive in defeat despite losing by mere millimetres to earn a second runner-up spot of the race.
"I'm second again but closer to the win than the day I lost to Theo Bos," he said. This is still my first week back on the bike. It was a great sprint by Mark Renshaw. I was coming fast in the end but not fast enough obviously."
Thursday's stage five follows a 178km route from Marmaris to Turgutreis.