"I was the first correspondent ever to report from the wreck of the Titanic. So, naturally, I was excited," Dr Guillen, who at the time was science editor at America's ABC network, told BBC Radio 4.
He recollects that - together with diving partner Brian and Russian pilot Viktor - they went down in a small Russian submersible lowered from the Akademik Mstislav Keldysh research ship.
After touring Titanic's bow where "everything had gone well", the crew decided to head to the stern area some distance away.
The Titanic sank on 15 April 1912, after striking an iceberg. Before going down, the British passenger liner split into two parts.
"As we approached the stern area - flying over what's called the debris field - we were caught up... in a very fast-moving underwater current. So we ended up getting stuck in the propeller," says Dr Guillen, describing it as "huge".
"All of a sudden, there was just a crash. We just felt this collision, and all of sudden debris... just huge chunks, rusted chunks of the Titanic started falling on top of us."
'I had said my goodbyes in my mind' Dr Guillen, a physicist and now a best-selling author, remembers that "it was pretty clear to us almost immediately we were stuck".
He says the pilot, who used to fly Russian Mig fighter jets, was trying to jostle the sub out.
"It's like you get your truck, your car stuck in the mud: you try to go forward, backward, forward, backward. Just to try to dislodge yourself.
"We all fell silent. We didn't want to disturb or distract Viktor. And we knew we were in a crisis. So we just kept quiet."
The sub eventually managed to get out "through the skill of Viktor", says Dr Guillen.
"We were just fortunate. There was a better part of an hour we were stuck. And I already pretty much had said my goodbyes in my mind.
"I'll never forget this thought that came to my head: this is how it's going to end for you.
"But in the end, we sensed that something changed... there was a sense that we were floating."
The journalist recollects that all this was happening in complete darkness, as the pilot turned off the spotlight.
"We didn't want to say anything. I was like 'My gosh, is it possible that we are out of this?'
"Then I turned to Viktor, and I said: 'OK?' That was all.
"He only spoke broken English. And I'll never forget [how] he said this in a very low growling Russian accent: 'No problem.'"