As a non-researcher, how to tell new knowledge that the speaker might not know?
It's perfectly fine to use the question period to alert the speaker to other related work.  As with any question, try to keep it brief: one or two sentences.  I agree that a &quot;couple minutes&quot; is too long.  Here are some sample phrasings.

There is a recent paper by Jones and Smith on reticulated splines, in which they propose a method to solve the trolley problem.  Would this help to resolve the issue you mentioned in your talk?
Are you aware of the recent paper by Jones and Smith which gives a solution to the trolley problem?  This seems like it might helpful in answering your question of whether splines can be reticulated.
You mentioned that you need a solution to the trolley problem.  There is a recent paper by Jones and Smith which solves this problem using the method of reticulated splines.  Does that seem likely to be workable in this case?

It is a good idea to mention the names of the authors - partly to give them credit, and partly so that the speaker or other audience members can look up the work later.
Try to resist the urge to explain the related work in detail; the question period is not the time for that.  If there are significant aspects of the paper that are very relevant (special techniques, limitations, etc), you can mention them briefly (again, one or two sentences).  Otherwise, you can certainly approach the speaker after the talk is over, during a coffee break, etc, for further discussion.