Why does entropy allow heat to be converted to work? Physical chemistry has made me question everything.
Recently, I was thinking: "why is it even possible to convert heat to work?"
From what I learned, a heat engine can take energy in and convert it into work. However, heat can be defined as more "disordered" than work (because in heat, particles are more "random", but in work, they more "organized". Let me know if you'd like for me to elaborate).
So, if heat is more disordered, having more heat and less work means that there is greater entropy. Therefore, when we convert heat to work, we are decreasing the entropy, are we not? And it's not just the entropy of the system, but the universe (because we obtain the heat from the surroundings). 
So, if according to the 2nd law, entropy can only increase, how is it possible to convert heat to work? What am I understanding wrong?
 A: 
From what I learned, a heat engine can take energy in and convert it
  into work. However, heat can be defined as more "disordered" than work
  (because in heat, particles are more "random", but in work, they more
  "organized". Let me know if you'd like for me to elaborate
  U

You learned correctly.

Therefore, when we convert heat to work, we are decreasing the
  entropy, are we not?

Once again you are correct. However, a heat engine operating in a cycle can only convert part of the incoming heat from a high temperature source into work. It must discard the other part of the incoming heat to a lower temperature environment.  One version of the second law is it is impossible to operate an engine in a cycle where it exchanges heat with only one temperature reservoir and converts it completely into work. There must always be heat discarded to a lower temperature reservoir.

So, if according to the 2nd law, entropy can only increase, how is it
  possible to convert heat to work? What am I understanding wrong?

What you understand wrong is you are not taking into account the increase in  entropy of the surroundings due to the necessity of heat being discarded to the surroundings. Yes, the heat the engine takes from the high temperature environment decreases the entropy of the high temperature environment (turns disordered energy into ordered energy- i.e, work).   But the heat discarded to the low temperature environment increases the entropy of the low temperature environment. 
For all real (irreversible) cycles the increase in entropy of the environment due to the discarded heat is greater than the decrease in entropy of the environment due to taking heat from the environment to do work. Since for any complete cycle the entropy change of the system (heat engine) is zero, the overall change in entropy of the universe (system + environment) will be greater than zero.
The best you can do is for a reversible cycle, where the overall change in entropy is zero. The most efficient of the reversible cycles operating between two constant temperature reservoirs is the Carnot cycle.
If you need a specific example, I can amend my answer. 
Hope this  helps.
