use (primary test) || (secondary test) in your sort block:

my %hash = ( A => 91, B => 82, C => 1, D=> 44, E => 82 );

my @by_value = sort { $hash{$a} <=> $hash{$b}
                                 ||
                             $a cmp $b
                    } keys %hash;

print "$_ => $hash{$_}\n"
    for @by_value;
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