Teenage striker Divock Origi, a second-half substitute, scored the only goal of the game two minutes from time at the Maracana on Sunday to ensure Belgium will progress from Group H.
Wilmots' men have been billed as a side full of attacking flair with an outside chance of going all the way in Brazil.
However, just as in their opening victory against Algeria, they were not at their best in a slender triumph over Fabio Capello's team.
Belgium are on course to go through as group winners, nonetheless, and Wilmots believes they were worthy victors against Russia.
"Mission accomplished, but it was really tough." said the Belgium coach.
"It was a very tactical encounter and the substitutions made the difference. It was a difficult test, but we deserved the points.
"You don't always have to be pretty, you just have to be efficient. We were stronger physically.
"Now we can celebrate a little and enjoy the victory. But it is also clear that we must seriously prepare for the final group match (against South Korea on Thursday)."
Wilmots brought on Marouane Fellaini and Dries Mertens to great effect in his side's win over Algeria, with both finding the net.
And the coach's decision to bring on Origi for the ineffective Romelu Lukaku 10 minutes into the second half against Russia proved to be another masterstroke.
The Lille striker was on hand to finish after great work from Eden Hazard and Wilmots was delighted to be rewarded for putting his faith in the youngster.
"Origi is only 19 years old and he was fantastic to get that goal." Wilmots added.
Lukaku cut a frustrated figure when he was replaced by Origi, but Wilmots refused to criticise the Chelsea striker for his reaction to being substituted.
He said: "Of course he's not happy. It's not a problem."
