The Poppies were playing their eighth away game in a row in all competitions against a side who are sitting in second place in the Evo-Stik Southern League Premier Division.
Law’s team made the perfect start with Spencer Weir-Daley giving them the lead just five minutes into his debut for the club.
The hosts had Matt Smith sent off during the first half for a foul on Chris Carruthers but they still piled the pressure on Kettering in the second period.
However, the Poppies absorbed all that and then rounded things off late on when Wilson Carvalho added the second when he fired home after Elliot Sandy’s header came back off the post.
And Law was a happy man as the Poppies got their bid for a play-off place back on course.
“It was a tough day,” he said.
“It was always going to be difficult with the way our season has been on-off for the past few weeks.
“Chippenham have been in great form. They are second in the league, they had scored something like 20 goals in their previous five matches, they’re well organised and know how to play their own pitch.
“Even though they were down to 10 men, we had to defend really well for a long time in the second half because they really came at us.
“But I have to give a lot of credit to our goalkeeper (Craig Hill) and the back four because we were very solid.
“Having said all that, some of our approach play at times was very, very good.
“That was certainly the case for the first goal. It was a lovely move with James Brighton’s pass, Liam Canavan’s dummy and then Wilson’s lofted pass for Spencer who has taken it on his chest and then volleyed it in.
“The lacks of games recently has hurt us but, on this occasion, we hung in there and produced a great all-round performance.”
Law, meanwhile, was pleased to see Weir-Daley, who has joined on loan from Corby Town for the remainder of the season, make an immediate impression.
“I think that was the perfect introduction to our supporters,” the Poppies boss added.
“He has come here from another local club and we know he can score goals.
“Him and Wilson are good players who may got a certain time with not affecting the game but they can come up with moments that will change things and that’s what happened.”
The Poppies will now be hoping to play their first home game since December 5 on Tuesday night with struggling Frome Town being the visitors to Latimer Park.