His momentum was halted by his first bogey at the 14th, where his approach nestled in deep greenside rough, but he was a picture of contentment afterwards.
"I played really well today," Woods told CBS television.
"I hit the ball so crisp and so solid and made some nice putts there on the front nine and had things rolling for a little bit."
Woods will have a week off before heading to Pebble Beach, the seaside California course where he won the 2000 U.S. Open by an astonishing 15 strokes.
Woods won the Masters in April, his 15th major title, but missed the cut at the PGA Championship at Bethpage two weeks ago.
He was feeling under the weather at Bethpage and was clearly a little rusty after not having played a tournament in more than a month.
The 43-year-old was determined to go into the U.S. Open prepared and his trip to the Jack Nicklaus-hosted Memorial served its purpose.
Woods is second on the all-time major championship victory list, three behind Nicklaus.
"I wanted to have something positive going into the Open and kind of sneak up there with a nice little top 10 possibly," Woods said of his goal on Sunday.
"I was never going to win the tournament with where I was at. I wanted to get to double digits (under par) today and I did. I just didn't stay there."
(Reporting by Andrew Both in Cary, North Carolina, editing by Ed Osmond / Ian Ransom)
