Roughly:

use strict; use warnings;
use URI::Escape 'uri_escape'; 
use HTTP::Tiny;
use Try::Tiny;

my $api_key = 'Your Secret Key';
my $email   = 'example@example.com';
my $url     = 'https://api.zerobounce.net/v1/validate';
my $params  = '?apikey=' . $apikey . '&email=' . $email;
my $api_url = uri_escape( $url . $params );

my $ua = HTTP::Tiny->new( timeout => 15 ); # seconds

my $response_string;
my $api_error;
try {
    my $res = $ua->get( $api_url );
    if ( $res->{'success'} ) {
        $response_string = $res->{'content'};
    } else {
        $api_error = $res->{'status'} . ' ' . $res->{'reason'};
    }
} catch {
    # Handles exceptions
    warn 'Something really bad happened: ' . $_;
};

__END__
[download]

See HTTP::Tiny.

I'm not sure that you wanted the response content in your response string; if you really want the entire response you can get it with $res->as_string but you'd have to use a different HTTP library (e.g. LWP::Simple).

Hope this helps!