Strootman broke the deadlock early in the second half with a fine solo effort, robbing Lazio defender Wallace before calmly lobbing goalkeeper Federico Marchetti.
Radja Nainggolan then found the bottom corner from distance 15 minutes later to double the advantage, as Roma ran out comfortable winners.
"I don't remember it that well," Strootman said afterwards, when asked about his goal. "I won the ball and I thought Edin [Dzeko] was offside, else I would have passed to him as he always scores.
"I thought I needed to shoot and I scored. I'm pleased for the team and fans, who didn't come today but were there in Trigoria yesterday. As I've said, we need them."
The midfielder stressed the importance of winning the game not just for city bragging rights, but due to the current league standings.
“It was a special match but our league position was also important," he added. "We wanted to win and we worked very well.
"It's horrible to see our end of the ground empty but maybe they'll be in for our upcoming matches. Those who did come along were very important for us. These are three massive points."
Your next match is against AC Milan, Juve's main challengers along with you.
"There are other teams in there as well, including Lazio even though they lost today. It will be a great game against AC Milan. We want to win the match but for now we must enjoy winning the derby."
You're winning matches without playing brilliantly. Does that show you've made progress in terms of your mentality?
"We've always won on this ground and that's important. We must improve a number of things, for example our away form, but these three points are massive."
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