Wing Kyle Evans crossed twice as Llanelli secured the bonus point win needed to progress from Pool 6.
The win means Llanelli and Moseley both finished with 19 points apiece but it was Buchanan's side who were celebrating qualification.
"This pool has been really competitive and we always felt it was within our grasp," he said.
"The win at Gala last week set it up for us. It was still a big ask but that was about as good as we have played this year.
"The Hopkins boys gave us stability up front and we had some young players who played extremely well with Kyle Evans showing exceptional pace for his two tries.
"All-round it was a great performance from us."
Moseley had taken the lead with an early penalty and the home side had to wait until midway through the first half for their opening try, scrum-half Aled Davies diving over from a scrum.
Owen Williams added the extra two before setting up his side's second score.
The fly-half's break put flanker Dan Thomas clean through before the ball was given to fellow back rower Duane Eager to touch down.
A second Williams conversion made it 14-3 and a brilliant try from Evans saw Llanelli well clear at the break.
Llanelli were reduced to 14 early in the second half when Thomas was sin binned for repeated offside and the visitors took advantage with a try from wing Brad Hunt.
After returning from the bin, Thomas was soon back in the action and he went over for Llanelli's vital score at the start of the final quarter.
The try secured the bonus point before Evans added a spectacular second and prop Shaun Hopkins powered over for Llanelli's sixth try.
Moseley had the final word but Llanelli's place in the knockout stages was secure.