Michail Antonio and Jesse Lingard scored at the start of each half to leave West Ham nine points clear of Spurs with a third of the season left to play.
The joy of the West Ham players was evident at the final whistle and Rice explained how Mourinho provided them with extra motivation to get one over on Spurs at the London Stadium on Sunday.
“I read during the week that Mourinho said that, at the end of the season, there would be no comparison between where Spurs are going to be compared to West Ham and that they were going to overtake us,” the West Ham star told talkSPORT.
“You read stuff like that as players – I think he said it on the Spurs YouTube channel – you read that as players and you think, ‘Yeah that is going to make me go out there and prove you wrong’.
“You go out there and you want to put out an even better performance, so I think all the lads knew that. We wanted to go out there yesterday and really beat Spurs.”
Rice admits that the West Ham of last season may have “caved” after Lucas Moura pulled a goal back for the visitors.
“Obviously we played them at the start of the season and we came back from 3-0 down to draw 3-3, and yesterday was another top result,” Rice added.
“But it’s a London derby; knowing that should be enough to get you up for anything.
“We are going out there now and we don’t fear anybody. I think maybe the West Ham of last season would have caved in in that second half and conceded goals.
“But now it’s completely different and now, like you say, we won’t cave in to anyone.
“We can score goals; we’ve got quality up there at the attacking end of the pitch as well. Long may it continue.”
On whether he’s determined to hold onto a top-four place, Rice replied: “100 per cent, definitely I think I would be wrong to sit here and say that’s not something I am thinking about.
“I want to be in those places now, this is where this club deserves to be. It is a massive club, we’ve got the quality like I said and that’s where we need to be pushing.
“I think the next four games are going to define that. We have got City, then Leeds, then United and Arsenal.
“Four massive games, so if we get through these with a good amount of points then who knows?
“We will be down to single figures then [in terms of remaining games], and we will be able to start counting down to see how long we have to go.”