Ba put the hosts in front after 33 minutes after brilliantly latching onto a Shola Ameobi knockdown to volley past Andres Lindegaard.
A dominant performance in midfield helped Newcastle stay strong before Yohan Cabaye hit a stunning free-kick after half-time to double the hosts' lead before Phil Jones' late own goal compounded United's misery.
"Our performance last week against Liverpool was not good so we had to get the three points today,” Ba told Sky Sports. “We had to fight like it was our last game.
“I don’t really look at the opponents when I am playing. I just say to myself that I am going to be good today and give 100 per cent. I am only concerned about myself.”
Ameobi echoed his strike partner's thoughts, and believes his side's game plan of pinning United in their own half contributed to the victory.
“We wanted to start [the new year] as we mean to go on. We were disappointing against Liverpool, we didn’t really show up, so this was a great opportunity to go up against the champions and show what we are all about," said Ameobi.
"The crowd were fantastic today. They really got behind us.”
“We saw what Blackburn did to them last weekend and we felt that that was something we could work on. Obviously Yohan [Cabaye] scored a fantastic free-kick which always helps, but one of our main tactics was to get in behind them and squeeze them up the pitch, and it worked.”