As Jamie Mackie prepared to replace Dorrans, the champions moved in front once more.
West Ham had barely recovered from Dorrans' stunning opener before Thomas had doubled the home side's lead.
"It was a great trip and it's great to be involved with your country, " Dorrans told BBC WM.
Dorrans scored 17 goals for the Baggies last term as they were promoted back to the Premier League.
The Baggies went ahead against the run of play when Graham Dorrans smashed his free-kick into the left corner.
Dorrans, 22, was rewarded for a strong start to the season with a place in George Burley's team that lost 2-0.
An innocuous free kick was conceded on the edge of the box and Dorrans rifled an unstoppable drive beyond Neil Sullivan.
They won 2-1 at West Bromwich Albion but could have had Gary Neville sent off when he brought down Graham Dorrans.
Mowbray signed Graham Dorrans from the Scottish First Division club last summer and the midfielder has recently featured in the Baggies first-team.
Dorrans' free kick from the left caused yet more disarray in the penalty area, deflecting off Reid and into his own net.
Goals from Graham Dorrans, Jerome Thomas and a Winston Reid own goal gave the Baggies what looked like an unassailable 3-0 half-time lead.
"It took me a little while to get in when I came down, but I knew that was always going to be the case, " Dorrans added.
Then, by way of relief, Miller was sent sprinting down the inside-left channel and he and Dorrans found themselves two against two in acres of space.
"It's difficult for myself having just made it into the squad but the lads have to stick together and get behind the gaffer, " Dorrans told BBC Scotland.
Dorrans half-volleyed the ball into the roof of the Czech net from 10 yards from a cushioned Naismith header, but the effort was correctly ruled out for offside.
The chairman added that Dorrans was getting on with pre-season training and the club were expecting him to be an integral part of their upcoming Premier League season.
Midfielder Graham Dorrans was looking an assured figure for Di Matteo's men and he produced a delightful ball to find an unmarked Bednar, whose header was tipped over by Logan.
He collected a perfectly clipped centre from Graham Dorrans and, with the Blackpool defenders appealing for offside, he beat Richard Kingson with a low strike to score his seventh of the season.
Dorrans, who had been with Livi since the age of 13 and still had 18 months of his contract still to run, is the Scottish First Division club's top scorer this season with 10 goals.
"All of the staff have been under a lot of pressure, " said Zola, who most recently claimed he was not told the club would be making a bid for West Bromwich Albion midfielder Graham Dorrans.
The Hodgson era got off to a flying start when, after just three minutes, Dorrans found space on the edge of the West Ham penalty area before unleashing an unstoppable rising drive beyond Robert Green.
Di Matteo has made the most of the Scot's versatility, using him out wide, through the middle, and even in support of lone striker Roman Bednar in the Baggies' last game at Preston - a role Dorrans relished.
The relentless Albion attacks opened up the Cardiff defence again just before the hour as Bednar's presence created an opening for Dorrans but with a clear sight of goal and from 15 yards out, the Scotsman skewed his left-foot shot wide.
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