There are two common misconceptions about 'spontaneous reactions' in biochemistry.

1. Spontaneous reactions do not need to be catalyzed by an enzyme. In fact, almost all biochemical reactions need to be enzyme catalyzed and mutations causing loss of enzyme activity are usually serious problems for the organism. This is because living organisms need to carry out reactions with relatively low concentrations of substrates at constant pressure and at relatively low temperatures. If not for the pepsin and other digestive enzymes in your stomach, you would starve because the 'spontaneous' hydrolysis of your food would not be rapid enough to sustain your metabolism.
2. The cell cannot carry out reactions that result in an increase in free energy. In fact, many of the individual reactions in the cell have a positive standard free energy change. A common example of this is the malate dehydrogenase in the citric acid cycle which catalyzes the following reaction

This reaction has a standard free energy change of approximately +30 kJ/mol, but yet the reaction must proceed as written for the citric acid cycle to provide energy in aerobic organisms. In a mitochondrion, the metabolite concentrations are manipulated so that the [NAD⁺]/[NADH] is approximately 20 and the [malate]/[oxaloacetate] is >1000. These combine to make the actual free energy change negative and the reaction proceeds rapidly with the rest of the reactions in this oxidative cycle.