The 40-year-old recorded a final round of 73 to leave him one-under for the tournament, in a return to form following a poor start to the year.
Westwood told Sky Sports News: "It's progress I started to swing the club a little bit better, and it's my best result of the year. I'm trending in the right direction.
"I probably hit the ball better over the weekend than I did the first two days, and that was really pleasing. The golf course over the week played fair, but it was very near the edge and it's as hard as it's ever going to get."
The result leaves Westwood still searching for his first Major win.