The victory for the home side will see them start 2018 in the play-off places after an impressive run of eight wins in their last 10 games.
And Gallen was quick to praise the impact of Hawkins, who bagged both goals with his head.
Gallen said: “I’m very pleased with the attacking performance. Three hasn’t done us justice today, we could have scored more.
“They were excellent headed goals from Hawkins.
“I can’t say we have worked on him heading it in from where he did but it was a fantastic header.
“We were thinking he might take it on his chest but he did exactly what he wanted to do with it and put it in the bottom corner.
“He bullied their full-back on the back stick, which we know he is capable of doing.
“He has come back into the team and scored two great headers.”
Hawkins could have given Pompey an early lead after he was slipped in on goal by Brett Pitman but his effort was saved by goalkeeper Matt Ingram.
Northampton then took the lead through Chris Long in the 36th minute when he was played in by Lewis McGugan before calmly slipping the ball past Pompey keeper Luke McGee.
But the home side pegged the Cobblers back moments later through Matty Kennedy when he lashed his shot into the bottom corner after cutting in from the left wing.
And Pompey found themselves in front on the stroke of half-time when Hawkins produced an excellent looping header to beat Ingram.
The big centre-forward then wrapped the game up for Kenny Jackett’s team when he arrived at the back post to nod home Dion Donohue’s cross.
Northampton manager Jimmy Floyd Hasselbaink lamented referee Lee Swabey’s performance as his side slumped to their sixth away defeat in a row.
And Hasselbaink said: “I think we started really well, we had more of the game.
“We dominated in midfield and then we scored a brilliant goal which is what we have been working on.
“But then the referee lost a little bit of the game. We didn’t get the free-kicks that we needed to get and they scored.
“The second goal was a freak goal which was well taken by the boy and then we were up against it.
“It didn’t help how the referee played today, I think he spoiled the game.
“He was very inconsistent and I don’t want to make it about the referee but psychologically it is a hard one for us to take.”
Southend manager Chris Powell led the applause for Jason Demetriou after the right-back scored twice in the 3-1 win against Portsmouth at Roots Hall.
Morecambe boss Jim Bentley was the happier manager after Gregg Wylde's 90th-minute strike earned his side a point in their 1-1 draw with Forest Green.
Manager Gareth Ainsworth described Wycombe's 2-0 win at Cheltenham as a thoroughly professional performance.
Skipper Richard Wood scored the winner just before half time as in-form Rotherham pulled off a 1-0 victory at League One leaders Shrewsbury.
Accrington Stanley boss John Coleman was pleased with his side's second-half rally after they came from behind to draw 1-1 at gutsy Barnet.
Notts County manager Kevin Nolan thought his side were denied a stonewall penalty during their 0-0 draw with Newport.