Nigeria frontman Odemwingie marked his return from an injury lay-off with what proved to be the winning goal after just three minutes at Norwich, though he also missed a second-half penalty.
Long was a certain starter at Carrow Road as the £6.5million signing had been troubled by the calf problem which forced him out of the Republic of Ireland's recent Euro 2012 qualifiers.
He was passed fit, though, and the pair linked up well, stretching the Canaries defence as the Baggies battled through to a first Barclays Premier League win after three performances which had deserved more than straight defeats.
"I saw a lot of promise, a lot of potential," said Hodgson.
"It was Odemwingie's first start of the season after a long period of injury and for Shane, we were doubtful if he could take part because of the calf strain he picked up with the Republic of Ireland.
"All things considered, they did well - but I would like to think there is more to come from them and they can play even better together."
Midfielder Graham Dorrans also made his first league start of the campaign, and was desperately unlucky not to score in the first half when his 25-yard effort crashed against the post.
The Scotland international maintained that despite the Baggies not getting their just rewards in the opening three games, the team were not about to lose faith.
"We were always confident the results would come," he said.
"We have played Manchester United and Chelsea, two massive teams and were unlucky to lose against Stoke to a goal in the last minute.
"We had to weather the storm a bit at Norwich, but we were always confident we could go to places like that and get the points.
"We have a great bunch of lads and players in there who can win us matches."
There is plenty of competition in the West Brom midfield, with skipper Chris Brunt and James Morrison both starting on the bench after being in action for Northern Ireland and Scotland respectively during the international break.
Dorrans said: "I have not had many minutes this season, but now hopefully I am back fit and can stay in the team now.
"I felt okay, although I had a bit of cramp 20 minutes before I came off.
"Hopefully now I can continue to get fit and improve."
West Brom defender Gabriel Tamas caught Norwich striker James Vaughan with a stray elbow at a corner during stoppage time, an incident which appeared to be missed by referee Mark Halsey.
Vaughan needed hospital treatment on a severe gash to his lip, and even though Hodgson maintains the clash was unintentional, it remains to be seen whether the incident will be reviewed by the Football Association's disciplinary department.