The Midlands club travelled to White Hart Lane bottom of the league and without a win since he took charge in June.
But West Brom frustrated their hosts and got their reward for a disciplined display when James Morrison headed in a 74th minute winner, to the relief of Irvine.
"It's my most satisfying day in management for West Bromwich Albion," the Scot said.
"It's great to get that first win. Everybody makes such a big thing about it.
"I'll go back to that first game against Sunderland, when it looked like we were going to get that win on the first day and that would have avoided all the questions – so I suppose it puts that question to bed.
"But we can't rest on that, we have now got to back that performance up by getting other good results."
The pressure had been mounting on the former Everton assistant, particularly during home matches, but the momentum shifted in his team’s favour early in Sunday’s match.
Irvine added: "I felt that there was probably a moment midway through the first half when the atmosphere and the mood in the ground change because we had had a sustained period of possession and some pressure and that obviously then can spread around the ground.
"We have experienced that obviously, at home. Fans are going to respond to what they see at that particular moment."
Another key moment was the inclusion of England defender Joleon Lescott in West Brom's defence for the first time.
Lescott has struggled with fitness since signing from Manchester City but was a stabilising influence on his new team.
"We would have been taking a big risk if we put him in before he was ready," said Irvine.
"We already had one setback against Nottingham Forest and I have tried to keep saying to people that we want to put him in the team but we want to put him in the team when he is ready and we felt as if he was ready this week."
The result, West Brom's first win at Spurs in 30 years, lifts them off the bottom of the Premier League and out of the relegation zone.
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