Having lost the first two games of the best-of-five semi-final series, Valencia knew nothing other than a win would keep them in the hunt for a first finals appearance since 2003.
They were beaten 3-0 by Barca on that occasion, and they looked in danger of going down by the same scoreline on Tuesday, trailing 42-32 at half-time.
The visitors responded strongly, however, to stay alive in the series, which remains in Barcelona for game four.
Barca’s Joey Dorsey top scored with 20 points in a losing effort, but Justin Doellman – who netted 16 in their 60-59 defeat on Sunday – produced 19 points, well supported by Serhiy Lishchuk (16) to help Valencia to victory.
The hosts, who finished third in the regular season, have reached the final for seven straight seasons, will have another chance to make it eight in a row when the two sides meet again on Thursday.
Like Valencia, Unicaja came into their clash with Real 2-0 down, but pulled off an 88-75 victory at home.
Nik Caner-Medley (14 points, seven rebounds) and Fran Vazquez (14, six) were impressive for the winners, who head into game four – again in Malaga on Thursday – full of confidence.
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