Randall won a photo finish with Marit Bjoergen to secure her second successive title in the ladies' race while Joensson broke clear of the field on the home straight to win the men's.
With two sprint races left this season, neither can now be caught with Swede Joensson 230 points ahead of American Andrew Newell, who didn't make it out of the quarter-finals.
Meanwhile Randall is 208 points ahead of Justyna Kowalczyk, who failed to advance beyond the semi-finals, and her immediate feeling at retaining the World Cup sprint title was one of relief.
"If the finishing line was another five metres away it would have been really close but I am glad I hung in there," said Randall.
"It [winning the sprint World Cup title] is a huge relief and I can go on to the next few races and really enjoy it and have fun. It is a great honour to win it."
Joensson finished eighth in the sprint World Cup standings last season but was overjoyed to have kept the crown in Swedish hands with Teodor Peterson victorious 12 months ago.
"I felt good all day and I had really good skis. It was really tight coming down into the stadium area and high speed and everyone packs together," said Joensson.
"I tried to focus and see where the other guys were and hoped nothing bad happened. In the final I got a bad start and I was behind the leaders. It was tough but I am so happy."
Riikka Sarasoja-Lilja was the early leader in the women's sprint final while Bjoergen came to the fore on the climb however Randall was never far away.
It was clear her and Bjoergen would battle it out at the finish with the American leading the triple Olympic champion into the final straight.
Bjoergen kicked in an attempt to edge out Randall at the line but, despite her efforts, it came to no avail as the American won the lunge after a photo finish.
Randall's time of 2:41.84minutes was just 0.07seconds better than that of Bjoergen while Alena Prochazkova took third place, 1.26 behind in total.
The men's sprint final was far tighter however Ola Vigen Hattestad and Joensson were at the front as the raced entered the final metres in Lahti.
And at the very start of the final straight Joensson skipped around Hattestad and powered his way to victory by 0.72 with Finn Haagen Krogh in third.
- Sports & Recreation
- Marit Bjoergen