Elmander carved out several opportunities for himself in an eye-catching display at the Reebok Stadium and was only denied a goal by the efforts of Fulham goalkeeper David Stockdale, who was in the side in place of Arsenal target Mark Schwarzer.
The Sweden international has had a tough time justifying the fee - believed to be around £10million - which Wanderers paid to sign him in the summer of 2008, scoring only eight times in the Premier League since then.
But Elmander capped a decent pre-season with a goal in Bolton's final friendly against Osasuna just over a week ago and Coyle believes the 29-year-old is finally starting to prove his worth.
"I thought Elmander was outstanding and deserved a goal, but all credit to Stockdale, the biggest compliment I can pay him is that Schwarzer wasn't missed," Coyle said.
"I have always had belief in him. He came with a big price tag and a big reputation, and the only person who will change anybody's mind about him is Johan.
"I can certainly try and impart the knowledge and wisdom that I have picked up over the years, and I can try and give him confidence because I have belief in him as a manager, and I've shown that by picking him.
"But really, he's followed on from his performance against Osasuna. Then he went away on the international break so I was genuinely worried that he wouldn't be fresh.
"But I gave him the nod again and he was outstanding, not just in terms of his goal efforts, but his work rate in general for the team."
Bolton had numerous chances to make the breakthrough, but were thwarted throughout by a determined Fulham side, who stood firm to secure a point for Mark Hughes in his first game in charge of the Londoners.
"I have to give Fulham credit. It was probably a backhanded compliment to ourselves that they were quite happy to sit in and have that solid back line," Coyle said.
"But that is why they had success last year, because of how hard they worked and they have good players."