We study the dynamical evolution of globular clusters using our two-dimensional Monte Carlo code with the inclusion of primordial binary interactions for equal-mass stars. We use approximate analytical cross sections for energy generation from binary-binary and binary-single interactions. After a brief period of slight contraction or expansion of the core over the first few relaxation times, all clusters enter a much longer phase of stable "binary burning" lasting many tens of relaxation times. The structural parameters of our models during this phase match well those of most observed globular clusters. At the end of this phase, clusters that have survived tidal disruption undergo deep core collapse, followed by gravothermal oscillations. Our results clearly show that the presence of even a small fraction of binaries in a cluster is sufficient to support the core against collapse significantly beyond the normal core-collapse time predicted without the presence of binaries. For tidally truncated systems, collapse is easily delayed sufficiently that the cluster will undergo complete tidal disruption before core collapse. As a first step toward the eventual goal of computing all interactions exactly using dynamical three- and four-body integration, we have incorporated an exact treatment of binary-single interactions in our code. We show that results using analytical cross sections are in good agreement with those using exact three- body integration, even for small binary fractions, where binary-single interactions are energetically most important.