He responded with his first international try and a competent kicking performance in the 48-6 victory to give Hadden a selection headache for the rest of this month and the Six Nations Championship at the start of next year.
For the whole of his tenure, Hadden has opted for the tactical nous and kicking game of Australian-born Dan Parks in the pivotal position of stand-off.
But Godman's growing maturity may mean the Scotland coach opts for the greater flair and explosive running of the former Merchiston Castle captain.
Godman himself believes that he will continue to make progress if he is given further opportunities from the start.
He said: "There is always a big debate about the stand-off position because it is such a key role in the team.
"I was pleased with my first start and thought I played my way into it. We were a bit rusty as a team but it was a decent start for us.
"I'm pretty confident about what I can do and showed a bit of that on Saturday but there is still more to come and hopefully I can get another chance.
Hadden praised Godman for his contribution against Romania and hinted that the 24-year-old could be the man to spark his backline.
Scotland's relentless tackling has been the foundation for their success this year, victories against France, England and Italy being built on a rock-solid defence.
Hadden hopes to introduce a more expansive game to the national side in order to take his team to the next level and become a real threat at next year's World Cup.
Against Romania, debut tries from Johnnie Beattie and Rob Dewey in addition to a brace from Hugo Southwell set Scotland on the way to a comfortable win.
Godman and Dougie Hall then claimed their first international tries before Chris Cusiter rounded off the scoring with five minutes remaining.
Hadden said: "Phil is an exceptional talent. He went on his own on the first attack and I wondered what he was doing but once he got into his rhythm he created a lot of opportunities for the players alongside him.
"He made it extremely difficult for the Romanian defence by the way he attacked the line throughout the afternoon.
"We obviously want to score more tries and I've thought our attack has gone reasonably well over the past 12 months and it has created a lot of good field position for us.
"The next step, the challenge for the players is to turn that field position into tries. The more this side plays together the more clinical it will get.
"I think there is a lot of attacking flair in the side, the structure is reasonable and there is an attacking mindset in the players but we never want to forget our attacking chores either because that has been the basis of our recent success."