Spurs moved within three points of Manchester United after Jermain Defoe's 63rd-minute strike on Tuesday evening, and their chances of breaking into the top two will be boosted if the Red Devils fail to overcome Newcastle on Wednesday night as Harry Redknapp's men have a game in hand.
For the first hour of Thursday night's contest, Spurs looked anything but title contenders, with uncharacteristically sloppy passing and wasteful finishing a running theme throughout their play.
Indeed, Albion goalkeeper Ben Foster had only really been tested once by Rafael van der Vaart's clever flick before Defoe hit the winner by holding off four defenders and poking home from 10 yards with his back to goal.
But with home games against Everton, Wolves and Wigan coming up this month, Tottenham have a real chance to show they are serious challengers to City and United, and Hodgson believes Redknapp's men can win their first title in 51 years.
"They are serious contenders. They have proven that already," Hodgson said.
"There is no question about that. They win their matches. They keep putting pressure on Manchester City and Manchester United to win their matches and they are getting some distance between themselves and the chasing pack so they have to be very happy with their first 19 games.
"If they win their game in hand then it will all be a question of seeing which of the three or four teams will have the best last 18 games. The quality is there, the depth of squad is. It's a well-organised club and team. I wouldn't bet against them."
Spurs were outsiders to book a place in the top four, yet alone challenge for the title earlier this season when they began their campaign with two hidings from the Manchester clubs.
A remarkable run of one defeat in their next 17 matches has followed, however, leaving Redknapp extremely happy with his team's display in the first half of the season despite the laboured manner of their victory on Tuesday night.
"I don't know if we played like a title-winning team, but you are not going to rip teams apart every week," Redknapp said.
"If someone had told me at the start of the season that we'd be where we are now after 19 games, I would have said 'fantastic'.
"It has been a great first half for us. Getting through the first half of the year and being where we are in the league is amazing considering we lost the first two games.
"It has took some doing really. It's great. We are there or thereabouts. Nothing is impossible.
"We have a lot to look forward to in the second half of the season."
Redknapp was relieved to pick up three points after failing to apply pressure on the Mancunian pair by managing only a 1-1 draw at Swansea on Saturday.
"It was very important to keep up there and it was a hard night," he said.
"They set up to be difficult to beat. Roy had a few injuries and it was hard work breaking them down.
"I was worried. At half-time I thought they were sitting deep and there was no space to exploit on the counter-attack but Jermain has always been a goalscorer."
The win came at a price for Tottenham, with Sandro, William Gallas and Jake Livermore all coming off with injuries.
Sandro and Gallas look set for lengthy spells on the sidelines after both picking up suspected calf tears - something Redknapp could have done without given that Scott Parker is also carrying a knee injury which could keep him out of Saturday's FA Cup tie against Cheltenham.
"I think Sandro tore a calf so that will be a long one," the Spurs boss said. "It looks like Gallas (tore a calf) as well. He felt it go.
"They will have scans tomorrow [Wednesday]. We will have to wait and see. Jake got a bang in the mouth - he split all his lip. He will have it stitched up. It doesn't look good.
"That leaves us short. I'm not sure how long Scott will be out for. His knee was swollen up today [Tuesday]."