After starting the day in second place overall, two seconds behind the race leader, Impey knew he had the opportunity to take the leader's jersey and went on to do so by taking valuable bonus seconds on the finish line.
The 33-year-old is the first South African rider to wear the Criterium du Dauphine leader's jersey and it is the second time Mitchelton-SCOTT has held the race lead in the French tour.
Four riders created the main breakaway of the day on the second, 177 kilometre stage from Montbrison to Belleville en Beaujolais.
Antoine Duchesne (FDJ), Pierre-Luc Perichon (Vital concepts), Frederik Backaert (Wanty-Gobart) and Nikita Stalnov (Astana) worked well together to open up a solid lead, gaining a maximum advantage of over six minutes after the first 50km of racing.
As the race rolled over the third category climbs, the current race leading team, Team Sky, led the gradual chase and caught one of the breakaway riders with 40kilometres to go and two more remaining escapees with 18 kilometres remaining.
As the race headed into the final 10 kilometres, the pace was high but one breakaway rider still remained in front. Stalnov battled on ahead, making hard work for the Australian outfit.
Fully committed to the plan, Mitchelton-SCOTT sat at the head of the peloton leading the chase with four and finally reeled in the leader with just one kilometre to go.
Impey was able to surf the wheels in the closing few hundred metres to finish in third place and sweep up the bonus seconds he needed to leap-frog Michal Kwiatkowski (Team Sky) in the general classification.
Kwiatkowski suffered a fall in the final kilometres and finished behind the peloton, however, with the three kilometre rule in place, the Sky rider remained on the same time as the bunch and finished the day in second place overall behind Impey.
Yesterday I had a great day and today we decided to take the initiative and go for the jersey. We did a lot to bring it back and then I had a good enough sprint to take some bonus seconds.
We have a great team for the coming team time trial, we have to be the fastest of course to keep the jersey. We have to try to get the biggest margin possible over the other GC guys and we will certainly be giving it our best. Daryl Impey - Race leader
1. Pascal Ankermann (Bora-Hansgrohe) 4:19
2. Edvald Boasson Hagen (Dimension-Data) ST
3. Daryl Impey (Mitchelton-SCOTT) ST
General classification after stage 2:
1. Daryl Impey (Mitchelton-SCOTT) 8:51
2. Michal Kwiatkowski (Team Sky) +0:02
3. Gianni Moscon (Team Sky) +0:05