According to North Dakota State University, the DNA replication process in eukaryotes occurs and finishes quickly because of the highly specialized sub-processes involved in synthesizing a new DNA strand to match the original strand of DNA.
First, in the G1 stage, the cell is enlarged to ensure easy replication. In the following stage, stage S, DNA helicases methodically unwind the two strands of DNA that compose the template strand. This leaves two individual strands that each form a new template. Next, the individual DNA nucleotides are copied and paired with their complementary bases. New DNA nucleotides are composed using these complementary bases. This is post-DNA synthesis, or stage G2. Finally, at stage M, mitosis takes place, and the cell is replicated in whole.