A very experienced air carrier crew crossed BOS Runway 27 without clearance. The three pilot crew was very surprised at their complacency. The captain was also fatigued.

Narrative

Problem: Runway incursion -- crossing active runway without clearance. Aircraft pushed back from Gate at BOS approximately XA30 and called for taxi at XA34. Initial instruction was to 'taxi to Runway 33L; hold short of Runway 27.' Moments later; while on Taxiway K; instructions changed to accommodate arriving aircraft to 'taxi via Taxiways E; B; C.' which entailed transitioning to Taxiway E via E1. From the intersection of Taxiways B and C; I was following B757 out to the runway. We ran the taxi checklist on Taxiway C; changed over to Tower frequency; and followed the B757 all the way to the approach end of Runway 33L; crossing Runway 27 at approximately XA46 -- roughly 10-11 minutes after the initial taxi instructions were received. The B757 did not seem to slow or stop at the Runway 27 intersection; and I followed it across to Runway 33L. Tower radioed to expedite the crossing; and that was my first indication that I perhaps did not have clearance to cross. There was a small commuter aircraft on final to Runway 27 approximately 2 miles out. There was no go-around and no threat of a near miss. As I was taxiing onto Runway 33L for takeoff; Tower inquired if we were returning that day and requested a phone call (Tower provided a phone number) and said there was a 'possible pilot deviation.' I contacted the Tower upon arrival at destination. Contributing factors: pilot in command had worked 7 of the last 8 days; including 3 days of training/simulator requiring commute. Last 3 days required getting up at XA00 AM and driving 1 hour to airport for 1 day trip and then driving home 1 hour. 2 days prior to incident; the trip involved mechanical problem requiring an aircraft ship change; followed by reroute to Caribbean destination due to the aircraft not being extended overwater capable; resulting in over 9 hours of flying time round trip and arriving home over 2 hours late. The next 2 days; trips required XA00 AM get-up. I recognize pilot fatigue is insidious; and though I thought I was fit for duty on this day; obviously I was not as sharp as I could have/should have been. Also; when the taxi reroute instructions were given; we should have clarified the hold short instruction.