The following code assumes that the values are separated by white space (untested):

use strict;
my $input_file = 'foobar.txt';
open my $in, $input_file or die "Failed to read $input_file: $!\n";
my $max = do { local $_ = <$in>; chomp; [ split ] };
while ( <$in> ) {
  chomp;
  my ( $x, $y ) = split;
  $max = [ $x, $y ] if $y > $max->[ 1 ];
}
close $in;
print "max at ($max->[ 0 ], $max->[ 1 ])\n";
[download]

Update: Minor change to original snippet (first data point is now read outside the while loop), plus additional snippet for the case of ordered smooth data.