The only way is those damn mobile lounges. They run pretty often but it means a hustle. Depending on how far the arriving gate is from the connector. The corridors are long at IAD. If your times are legit, you're supposed to be able to make - there have been times than my arrival time (touch down) is about the time my departure flights starts boarding. And the taxi times in IAD are unpredictable and can be as long as 15 minutes plus. Other times I have been at the gate less than five minutes after touch down.
Good luck!