The England winger made just his second start of the campaign and put the disappointment of an injury-hit 12 months behind him by opening the scoring inside 90 seconds at the Amex Stadium.
It was Walcott's first strike since New Year's Day 2014 and he admitted his relief at ending the goal drought after the game.
"It's been a long time coming," he told Arsenal's official website. "I had a lot of chances since I have been back, but I have been out for a year so it is still going to take time.
"It is just nice to get some match fitness back. I was very pleased with the finish and there will definitely be many more.
"People will be expecting me to score every game now but it’s all about getting the match fitness, sharpness and the goals back. The goal was a bonus.
"The goals will come but I'm just enjoying being back with the guys and working on my fitness, getting the sharpness right. I was blowing quite heavily towards the end but I was very pleased with the finish.
"The most important thing is that the team got through."
The result saw Arsenal take another step towards defending the FA Cup crown they won back in May with a 3-2 Wembley win over Hull City.
