This may be caused by not taking account of newlines on the lines read from the file. Include a chomp and see if that helps.

#!/usr/local/bin/perl

use strict;
use warnings;

my @array = qw{one three};

while(<DATA>){ 
    my $var1=$_; 
    chomp $var1;
    foreach my $var2 (@array){ 
        if($var1 eq $var2){ 
            print "line is $.\n"; 
        } 
    }
}

__DATA__
one
two
three
four
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