The duo are part of Team Mouat, representing Scotland in the World Championships in Calgary which is doubling as a battle as qualification for the Olympics.
A total of 14 countries are taking part with the top six from a round-robin event playing off for the title and also booking places for their countries at Beijing 2022.
And despite losing their latest match 9-2 to Russia, a defeat for rivals Norway means the team – with eight wins from 12 games – have done enough to secure one of the coveted top six spots.
Scotland bounced back from an opening defeat against hosts Canada to win their next four matches.
Skip Bruce Mouat and his team had looked to have the upper hand in that opener when they claimed a three at the fifth end to take a 5-2 lead at the halfway break.
However, after picking up a two at the sixth end, Canada moved in front with a steal of two at the seventh, which proved to be the turning point as they ran out 9-6 winners.
Next up for the Scots were Denmark, who had also lost their opener to neighbours Norway.
The Scots took an early advantage and although Denmark hit back to level the Scots regained control to run out 7-2 winners.
A demanding fourth day opened with a tough to take 6-5 extra end defeat at the hands of Sweden's reigning world champion Niklas Edin whose final stone denied the Scots who had been lying two.
But McMillan, Lammie and co rallied to pull off a brilliant comeback against Germany in their second match of day four to maintain their challenge for a play-off spot.
Germany, boosted by a first win of the competition over table-topping Norway, raced into a 5-1 lead but the Scots raised their game to force their way back into contention and eventually edged their opponents out 9-8.
Day five produced another two wins with McMillan and Lammie playing key roles in a 6-3 victory over Japan and a 7-4 defeat of fellow play-off contenders Switzerland to leave Team Mouat in joint second spot in the pool with four matches to play.
Wednesday’s schedule opened with the team suffering only their third defeat as the USA snatched a 10-9 victory with the final stone at an extra end.
But once again the team showed character as they bounced back to defeat Italy 7-2 and leave them on the brink of the play-offs.
Scotland have one more round-robin match to play, against Norway, before the play-off knockout matches get under way.