Air Carrier Captain reported they had to slow down significantly while taxiing to avoid collision with a tug pulling an aircraft across their path.

Narrative

Our flight pushed approximately two hours late to ZZZ1 due to air traffic control delays. There were no available routes to the south; so we shut down both engines for approximately 35 minutes while holding our position.We eventually received a taxi clearance northbound via Taxiway 1. We stopped several times for flow and congestion. The controller then amended our route to: Taxiway 1 (as it bears left); Taxiway 2; Taxiway 3; with the intent of getting us around a 737 ahead of us. We were then instructed to monitor Tower for XX R at Taxiway 4 departure.During this time; a SuperTug with a 737 was north on Taxiway 5. My attention was primarily on the 737 ahead of us; which was moving slowly; with wingtip to tail clearance my concern. The First Officer noticed the Super Tug approaching from our left on Taxiway 5. We had to slow significantly to avoid a potential collision. I flashed the landing lights; but the Super Tug appeared unaware of our presence.I believe the Super Tug had the right-of-way; as they were the first to receive a taxi clearance. The controller appeared to make an on-the-fly decision to get us around the traffic ahead of us. Frequency congestion was an issue; with a single controller working multiple issues during non-standard ops.I submit this report primarily as a data point. Had it not been for a sharp First Officer; and my general slow and steady taxi speeds this could have been a low speed collision.