Rooney nodded home the only goal against co-hosts Ukraine in Donetsk on Tuesday three minutes after the break.
The Manchester United forward, back after completing his two-game suspension, had earlier missed a golden opportunity, but did not let that affect him and has now scored 29 goals for England - just one behind Nat Lofthouse, Tom Finney and Alan Shearer, who are joint fifth on the all-time list.
"He's got character, hasn't he?" Hodgson said of Rooney. "Those who have followed England and Manchester United, even Everton, you know what Rooney is, what he can do and his qualities. He showed them in abundance tonight. He and [Danny] Welbeck worked extremely hard."
Hodgson had played down the length of Rooney's absence. However, after appearing for just 37 minutes since his final game for United on 13 May, the England coach was delighted he almost got through the entire match tonight.
"It was his first game after having to sit these two others out, and it is a while since he played a competitive match, so he's got to be happy with the way things went for him," said Hodgson. "Every day helps him and helps us. The fact he's had 80 minutes in this game will give him confidence going into the next game."
Hodgson was eager to spread the praise though, especially as captain Steven Gerrard collected the man-of-the-match award after delivering the cross for Rooney's goal. "You've got to single Steven out," he said. "He has built up to this man-of-the-match award in the previous two games as well, playing a captain's innings throughout.
"The back four were very good today, and the goalkeeper, they kept their shape and discipline extremely well. Although there were shots at our goal, they were from distance and didn't really necessitate [Joe] Hart to make saves. It was a game to praise the team performance."
Hodgson can now brace himself for an outpouring of national fervour as the country starts to believe it can finally win another trophy to go alongside that 1966 FIFA World Cup™ win. It is a far cry from the low expectations that accompanied England on their departure.
"After Fabio Capello resigned people thought the team wouldn't have enough time with a new coach to prepare," he said. "Luckily we've proved that to be wrong. I'm pleased about that. As far as our stays in Ukraine and Poland, I've been delighted with that.
"Now we are getting good vibrations from those back home. It's not really a question of expectations. We want to keep going and try and enjoy this tournament for as long as we can."