The hosts shot out to a commanding 20-point lead (53-33) at half-time and it appeared it would be Adelaide by how much.
But the Tigers had other ideas and sprang to life after the major break and got within a point (85-84) after Adam Ballinger (16 points) drained a three-pointer with 1:51 left in the match.
However, that was as close as the visitors would get as Adelaide held on for a nail-biting victory.
American import Gary Ervin top-scored for the 36ers with 21 points and eight assists while Daniel Johnson (19 points and six rebounds), skipper Adam Gibson (13 points, five assists and three steals) and Luke Schenscher (11 points and seven rebounds) all contributed too.
Mark Worthington was outstanding for Melbourne with 28 points and eight rebounds and he found sound support in the form of Chris Goulding (23 points and five assists), Ballinger and Nate Tomlinson (15 assists).
In other results on Friday night, the Sydney Kings rode captain Ben Madgen's 31 points on the way to their 99-86 victory against the Cairns Taipans at the Sydney Entertainment Centre, while Brian Conklin (33 points) guided the Crocodiles past the New Zealand Breakers 91-78 in Townsville.