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Ba's curling opener from the corner of the box in the 55th minute lit up a low-key encounter and sparked the late drama in which Jermain Defoe bundled a 76th minute equaliser and Hatem Ben Arfa slotted a penalty winner four minutes later.
The excitement was too much for Pardew, who despite urging his players to keep their cool in his programme notes, lost his own when confronting the linesman over a touchline incident and was sent to the stands.
Pardew said: "There's me telling my players to behave themselves and follow the Olympic spirit and be humble, and they did it except for me.
"It was a stupid moment - the linesman just happened to be standing right in front of me when I thought the ball was out, and I gave him a little shove. I have apologised and I can't turn the clock back, so I will have to take my punishment."
Pardew singled out the performance of Ba, whose contractual situation has left his Magpies future in doubt, insisting the player has always remained at the forefront of his plans despite his long spell without a goal.
Pardew added: "It probably was important for Demba but only in terms of goalscoring. He has been brilliant for us when we have asked him to play on the side and he has done it again today and come up with a goal.
"It was the first game of the season today and I think it just showed that sometimes it is character and spirit that can win through. We had to match what Spurs were doing, we changed things at half-time and I thought we just about edged it."
Disappointed Tottenham boss Andre Villas-Boas reiterated his desire to boost his squad with a new striker but insisted any such move was not dependent on the completion of Luca Modric's move to Real Madrid.
Villas-Boas shrugged off reports of a hitch in the Modric deal, saying: "At this moment it is in the chairman's hands and obviously he is not here to explain the contents of the deal. We are looking to conclude the deal if it is in the interests of Tottenham.
"But the money we need to invest is not dependent on Luca's transfer. For different reasons it has not been possible to conclude the deals we have tried to do, so we continue to look for it to be done in the coming week."
Villas-Boas refused to give his opinion on the penalty incident but admitted the result was "hard to take" after his side worked so hard to drag themselves level within four minutes of Ba's excellent opener.
The Portuguese added: "I think our first half was really good with the amount of chances we created, and in the second half we had the same consistency but Demba Ba made the most of that split second with an excellent goal.
"We came back into it playing good, attacking football and we got the momentum back at 1-1 and it's a shame we couldn't keep it. It is obviously hard to take but the manner of the performance eases our pain a little bit."
The result was perhaps harsh on Tottenham who made most of the running and also hit the woodwork through Defoe, but Newcastle captain Jonas Guttierez was only interested in the result.
"Tottenham are a really good team and it was important to start with three points," he told ESPN.
"We are happy with the team and we had to win. We had a few chances, they did, and we took the opportunity to take three points."
Ba's goal was a welcome return to form for a man who was sensational for the first half of last season but played second fiddle to Papiss Cisse after Christmas.
"It was a good game for us. It's our first game, we got the three points and it's always important to have a good start. It is always very good," he said.
"It was very important to get a goal, but I am not running only for goals. The more I play well, the more the team wins. But, it's my first goal and I am very happy."
