The home side went into the break 13-6 up courtesy of a solo try from winger Tom Brown, converted by Greig Laidlaw, who also added two penalties.
Perpignan's reply came in the form of two successful penalties from James Hook and a further effort early in the second half drew his side closer.
However, Edinburgh flanker Cornell Du Preez barged over from close range, before Tom Brown touched down after a kick ahead from debutant Carl Bezuidenhout.
Laidlaw added both conversions, but his side failed to grab a bonus point. However, Solomons was refusing to be downbeat with qualification for the European Challenge Cup still on the cards.
"I thought we played well," he said. "That was a really good performance by the team. It was a tremendous defensive effort but overall a really good performance and we deserved the result.
"I thought maybe in the opening 20-25 minutes we were making the tackles but we weren't stopping momentum and we had a high error rate.
"But I thought we built into it and once we got our rhythm defensively I thought they found it very difficult to score.
"We had three opportunities to get the (bonus point) try. We went for it. Unfortunately, on the night we didn't get it but I don't think we should let it detract in any way from what was an outstanding performance."
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