Try this. Nonblocking read is necessary.

#!/usr/bin/perl
use strict;
use warnings;

use IPC::Open2;
use Fcntl qw(F_SETFL F_GETFL O_NONBLOCK);

my ($rh, $wh);
my $pid = open2 ($rh, $wh, "sftp somehost") or die "can't sftp: $!";

my $flags = fcntl ($rh, F_GETFL, 0) or die "can't get flags: $!";
fcntl ($rh, F_SETFL, $flags|O_NONBLOCK) or die "can't set O_NONBLOCK: 
+$!";

print $wh "ls foo\n";

my @files;
my $ln;

while (! ($ln = <$rh>)) {}    ## wait for valid output
do {
    $ln=~/.+sftp>\s*//;   ## eat sftp> prompts
    chomp $ln;
    push @files, $ln;
} while ($ln = <$rh>);

for (@files) {
    my $qf = quotemeta;
    print $wh "get foo/$qf\n";
    print $wh "mv foo/$qf bar/$qf\n";
}

print $wh "bye\n";
waitpid $pid, 0;
[download]

I couldn't test this 100% as-is but a similar version worked.

Edited (twice) to ignore sftp> prompts.