"It's an enormous, enormous, enormous three points, which gives us a lot of encouragement and hope going forward," Allardyce told reporters.
Swansea went into the halftime break a goal ahead despite going down to 10 men after Kyle Naughton was sent off, but two second half strikes from Defoe were enough to seal the Black Cats' second consecutive league win.
Allardyce revealed how he had tweaked his tactics at the interval to make the most of the one-man advantage.
"Halftime for me was about the lads doing their jobs properly and pressing, a high press which is not something we usually do away from home," he said.
"Playing against 10 men, we had to shut Swansea down in their own half every time they tried to play.
"That's what worked for us in the end and the clinical Mr Defoe has won us another game."
The manager reserved special praise for Defoe, after the striker added a hat-trick to his brace against Aston Villa on Saturday.
"We're putting the myth to bed that Jermain can't play up front on his own because he's won us two games now," Allardyce said.
(Reporting by Simon Jennings in Bengaluru; Editing by John O'Brien)
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