The United record is between 5 and 3 for Sunday against Cairns.
Despite the absence of star protector Chris Goulding (knee injury), visitors jumped confidently to 15-11 before the Hawks will be closed with an increase of 15-4 to 25-20 minutes per fourth.
Coenraad had his hand warm with nine points, while DJ Kennedy went to Melbourne with seven.
The Hawks controlled the opening minutes of the second period, extending the margin to 11.
But when they were on the way to building a great half-point lead in two games, Melbourne lifted the bar and cut the deficit to four.
Illawarra recovered the momentum to overcome 51-42 at rest, helped by a technical foul called Melbourne coach Dean Vickerman at the end of the quarter.
Illawarra continued playing his stellar opponents, taking advantage of 72-59 in the final period and responding to all the challenges in the stretch.
The Hawks return Sunday with another game against Perth.
Illawarra's victory won two previous defeats to Melbourne this season.
"They came out with a lot of energy and intentions and we did not do it with them all the first part," said Vickerman.
"We came back and we still had some decent looks to win the game but they deserved it.
Vickerman expects Goulding to play on Sunday.
Illawarra's coach, Rob Beveridge, was proud of his team's performance after two casualties.
"There was a bit of hatred of our own fans that is quite disappointing," said Beveridge.
"We had to prove to ourselves that we can compete with any team in the league and prove that tonight.
"Dave returned the clock and was absolutely exceptional. His conversation, his leadership – that fabulous performance of a block that is 38. It did not look like 38 tonight."