Cavendish had earlier picked up bonus seconds at both the intermediate sprints, finishing second to Kristoff at the first one before winning the second.
Both were buoyed by the lightning-fast start to the day’s stage which saw the peloton fracture and a 21-man group go clear – their advantage stretching out towards the minute mark and holding steady.
The pace stayed high, though a puncture for Farrar proved only a slight blip as the American rejoined Cavendish and Boasson Hagen in the front group.
Some riders did find the pace too hot to handle, however, with BMC Racing and Team Katusha in particular driving a fierce pace as the crosswinds became headwinds.
Katusha delivered Kristoff in pole position but the Norwegian could not up the tempo as he looked to lead out the sprint.
Instead it was Cavendish who kicked hardest, and the Manx Missile will swap Dimension Data’s white-and-black kit for the gold jersey on stage two.
Tour of Qatar 2016: stage one – result
1) Mark Cavendish (GBR) – Team Dimension Data – 3.28.46hrs
2) Sacha Modolo (ITA) – Lampre-Merida – ST
3) Andrea Guardini (ITA) – Astana
4) Sam Bennett (IRL) – Bora-Argon 18
5) Alexander Kristoff (NOR) – Katusha
6) Edvald Boasson Hagen (NOR) – Team Dimension Data
7) Greg van Avermaet (BEL) – BMC Racing
8) Manuel Quinziato (ITA) – BMC Racing
9) Arnaud Gerard (FRA) – Fortuneo-Vital Concept
10) Soren Kragh Andersen (DEN) – Giant-Alpecin