How can a case be dismissed prior to trial due to defendant committing perjury in his answer to summons and complaint?

Not going to happen. That's what trials are for. To prove or disprove the allegations in the complaint and/or answer. Your defendant is going to have to prove the affirmative defenses in his answer, just as you are going to have to prove the allegations in your complaint. Like I said, that's what trials are for.

The Defendant has to prove the case. It cannot be dismissed due to an Answer. Did you make a timely motion to set trial?

You do not know how the court system operates. A defendant is allowed to raise defenses that are untrue and even if he makes false statements under oath it is not treated as perjury. The only way to get a judgment without trial [unless his answer is stricken, so liability is deemed admitted, but you still have to prove your monetary damages], is by a motion for summary judgment which requires something like a $700 filing fee and at least 75 days notice to the defendant, so is not a speedy remedy]. You need to read some books, such as those from Nolo Press, as to how to handle an unlawful detainer case, and it would be best if you go to court and watch 1-2 to see how they are actually handled. The legal system does allow tenants to drag out their evictions; even if the judge rules entirely in your favor, they may grant the defendant extra time to find a place to move to. Tell the defendant that if you get a judgment instead of their moving out on an agreed upon date, the judgment will adversely affect their credit rating and make it difficult to find a new place to rent.