You can do this with BBMap's "FilterByName" tool:

filterbyname.sh in=x.fastq names=y.fastq out=z.fastq include=t

But, whether you SHOULD do that or not depends on your goal. Are you, perhaps, trying to fix a situation where you had paired reads in two files, and one of the files is missing some of the reads? If so, they were processed non-optimally; the better solution is to start over with the original raw reads and process them in a way that keeps reads together and maintains the correct order. Can you explain the situation in more detail?

If you can go for alternative solution, use the following oneliner

Check starting letters of the each read id in file2 and use first 4 or 5 letters to extract ids.

grep '^@HWI' file2.fastq | xargs -I {} grep {} -A 3 -m 1 file1.fastq > new.fastq

using the join operator:

 join -t '       ' -1 1 -2 1   <(gunzip ids.fastq.gz | paste - - - - | cut -f 1 | LC_ALL=C sort | uniq) <(gunzip -c  reads.fastq.gz | paste - - - - | LC_ALL=C sort -t '       ' -k1,1) | tr "\t" "\n"

Unless you're filtering the reads you're keeping from file 2 by quality, or using another program that requires fastq input, it would be easier to parse a fasta. However, this is how I would change your above code. The output is in fasta format.

def make_dict(seqs):
     d = {}
     for n in range(len(seqs)):
             d[seqs[n].id] = str(seqs[n].seq)
     return d

read1_in_handle = open("new_read1.fastq","rU")
    read2_handle = open("read2.fastq","rU")
    read2_out_handle = open("new_read2.fasta","w")

    read1_records = SeqIO.parse(read1_in_handle,"fastq")
 read2_records = SeqIO.parse(read2_handle, "fastq")

read1_dict = make_dict(read1_records)
read2_dict = make_dict(read2_records)

for i in read2_dict:
     if i in read1_dict:
          print >> read2_out_handle, '>' + i, '\n', read2_dict[i]

read2_out_handle.close()