Drivers were warned to avoid the area by Highways England.
Damien Cameron, a firefighter in West Yorkshire, described the incident as a "very lucky escape" - with no serious injuries reported according to his update.
The collision sent the HGV and trailer over the edge of a bridge on the M62, Mr Cameron said.
He told how a courageous passerby had helped before the emergency services arrived.
In a tweet, Mr Cameron said: "Incredibly lucky escape.
"Thankfully no serious injuries after a collision sent an HGV & trailer off a bridge on the M62.
"Passersby quickly gave assistance until Police, Ambulance & Fire crews arrived on scene."
The road reopened at 5.30am on Tuesday, May 11.
Highways England said: M62 westbound full closure J31 to J30 has now been removed.
Their update said: "Traffic is flowing freely in all lanes."
A spokesperson for West Yorkshire Police said: "At approximately 8.16pm last night, police in Leeds received reports of a road traffic collision involving an HGV lorry on the M62 westbound, between junction 30 and 31, Rothwell.
"Officer attended and found the HGV had left the carriageway onto the Aire and Calder Navigation.
"The driver and passenger of the HGV were taken to hospital with injuries not believed to be life threatening.
"The motorway was subject to closures for some time but has now been reopened."