LA Galaxy's Beckham delighted with scoring performance
He was eventually substituted in the 63rd minute but the performance will do the former Real Madrid and Manchester United midfielder's chances of a 97th England cap no harm, with the 32-year-old expected to be named in McClaren's squad on Friday for the friendly with Germany at Wembley the following Wednesday.
Beckham, who was visited by McClaren in the United States last week, said: "I was happy to get an hour on the pitch.
"I didn't expect to last an hour but it felt great after 10 minutes into the game.
"It was important for me to actually get on the pitch and play some minutes. I think that was the most important thing for me.
"I knew once I'm on the pitch, I know I can play well and help the team and that's all that was on my mind tonight, helping the team and helping us get into a final and helping get our season under way."