The striker, who turns 28 on Thursday, weaved his way into the box after just two minutes and saw his shot cannon off the goalframe before being diverted into his own net by the hapless Inigo Martinez.
The result keeps United one point clear of Bayer Leverkusen - 4-0 winners over Shakhtar Donetsk - at the top of the section.
"We should have won the game by three, four or five goals. But I'm happy we got the win which was most important after Saturday," Rooney told Sky Sports.
"We played some great stuff and defended well. A clean sheet is always pleasing but the three points were the main thing tonight.
"We got an early goal. We could have gone in at half-time 2-0 up and the game would have been more comfortable for us.
"But we didn't and started the second half a bit slow."
Manager David Moyes also paid tribute to the striker's overall display.
"He was absolutely terrific tonight," he said. "I was shouting at him in the last five minutes though.
"We just want a top player like Wayne to play well. I said from day one that his training was great. I think England have seen that. But we need to see it all the time."