"It felt good but it's fun to go out on links and for me to hit shots and they don't necessarily have to be spot on", Fowler said.
Stenson, now ranked seventh in the world, missed the cut at the recent US Open but bounced back to form a week later in Munich, finishing 10th in the defence of his BMW International Open title.
Fowler, who won the Scottish Open when it was held at Gullane, missed the 2016 tournament because of scheduling conflicts arising from the Olympics in Rio de Janeiro, which clogged up the golfing calendar last summer.
After England's Callum Shinkwin had set the early clubhouse target after he eagled the last to complete a 67, Fowler outshone playing-partners McIlroy and Henrik Stenson and the American was one of only four players in the 156-man field to keep a bogey off his card.
"I enjoy playing the week before the majors just to get myself ready to go, check off some boxes".
Rory McIlroy vented his anger with an F-Bomb en route to shooting an opening 2-over 74 at the Scottish Open.
Illonen's fortunes could not have been more contrasting, a run of five birides in six holes on his back nine helping the Finn move clear at the top of the leaderboard. His highest finish in 2017, however, was tied for 32nd in Dubai.
He and his wife Erica took the two-hour ferry from Belfast to Cairnryan in Scotland on Monday, with McIlroy heading straight to the practice putting green upon his arrival."After catching the ferry, I got to the course here late Monday afternoon and did some putting on my own", said McIlroy, who recorded 33 putts for each of his two rounds in Northern Ireland last week.
Adam Scott swells the regular ranks of Australians on the European Tour this week when he tees up at the Scottish Open as part of his final preparations for The Open Championship.
Scott has practised already at Royal Birkdale, venue for next week's Open Championship, and will from Thursday tee it up on the Scottish west coast for the $7 million event being staged for the first time on the Dundonald links.
Dalmuir Golf Club's Stewart Savage also missed out on a chance to play at the Scottish Open.
Adam Scott is playing the event for the first time since 2009, while Rickie Fowler the 2015 Scottish Open champion is back after missing previous year because of the busy summer schedule arising from golf being played at the Olympics.