United were trailing thanks to a Justin Cochrane strike, but Matty Sparrow hit a quickfire leveller and goals from Richie Hinds and Andy Keogh sealed the win.
Laws said: "I'm very pleased with the result - it will give us a huge psychological lift.
"It's dog eat dog down there, but we just need to keep playing the way we can to get ourselves out of trouble.
"We started the second half as we meant to go on and got the third goal that made it hard for Gillingham to come back.
"It was refreshing to kill a team off for good, the secret was hard work.
Laws: Hard work paid dividends
"The first-half was dire and it needed the goals to kick-start the game, I was a bit disapointed with their goal as the midfield player went through and we didn't pick him up.
"But it was a terrific goal from Sparrow and we stepped it up in the second-half.
"For the second goal it was a great delivery from Baraclough, and I thought Hindsy was superb. My decision to put him into midfield and put Andy Crosby in the back for his organisation proved a point.
"Our defending was excellent, and that's the way we're going to have to be. Everything they threw into the box we reacted to it, we've earned that result and deserve it."
Gills boss Ronnie Jepson said: "I don't want to name players but I have done in the dressing room and they will see that one again on the training ground.
"We're always trying to take positives but we have to look at the negatives and work on them.
"That performance wasn't good enough for me or the spectators. They let their feelings known at the end and I don't blame them.
"It was a poor result - we started quite brightly but I think what did us was our defence which was all over the place.
"The space we gave them was quite unbelievable and when you give them that much space you're asking for trouble.
"We had injuries and suspensions but that does not detract from the performance of the back four which gave them the initiative.
"I've seen the third goal on video and it was quite incredible how badly we defended."