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Keith Southern had given Blackpool the lead but two strikes from Roman Bednar gave the promotion hopefuls the lead.
Stephen Dobbie levelled after 80 minutes only for Dorrans to end the hosts' hopes from the spot.
Baggies manager Di Matteo said: "This was a really hard fought match. We have to dig in and fight for the points. Not many teams come here and go away with anything but I am delighted with my players' performance.
"We took our chances well and Roman Bednar did his job up front with two well-taken goals."
Both sides started tentatively on a pitch which had been covered in snow until just before the kick-off.
But Blackpool went on to play some attractive early football and kept pressuring West Brom for the majority of a game that saw plenty of action at both ends.
Tangerines boss Ian Holloway was left angry about what he perceived to be a poor penalty call after Ishmael Miller went down with Andy Butler in attendance.
"I said before the game that our next two matches could be defining. It is a shame we had to lose this one on a referee's penalty decision," said Holloway.
"My lads are shattered about that decision because they thought it was a fair tackle.
"However I thought we did well against a side I consider to be the best in the Championship. They have a class squad based on established Premiership players and we gave them a really good run for their money. They know that.
"We will have to see how the next couple of games go but my target for the season was always going to be 52 points and safety. That remains my target, anything else is a bonus."
Source: Team Talk
Source: Team Talk