Yes, this sounds like a case for multiple regression.
Is it thought that they both explain the same variability in the dependent variable? Or is it that they are both on the same causal path. And if so, does the further up stream variable have its own direct effects on the dependent variable or is it mediated through the intermediate variable. If it is this later scenario, you may need to run mediation analysis to parcel out the direct and indirect effects of the variables. Which this includes running a couple of regression models.
Lastly, you sound like you don't know how to do multiple logistic regression. What is your background and confidence level? Also, how are all of these variables formatted, are they categorical variable, continuous, or ordinal?
If they are both in the model, you are controlling for them. One thing that some people neglect to do, is that if you have an interaction term in the model you still need to keep the two base terms in the model as well. So if you have: y-hat = Bo + B1(X1) + B2(X2) + B3(X1*X2) model you should be good. I don't work with many continuous variables, but I believe it is good practice to center your continuous predictors when you have an interaction term in the model (and some may say to do it all the time).
Feel free to upload your outputted results to better help us understand what you have done and what the results looked like.