Up at the front, however, Vettel emphasised his dominance by opening up enough of a lead to enable him to make his second pit stop and rejoin still at the head of the field.
Grosjean ran a long middle stint and moved up to second position when Webber and Rosberg pitted for the second time. When he finally pitted on lap 38, the Franco-Swiss driver emerged side-by-side with Felipe Massa, and narrowly fended off the Brazilian, who came in for new tyres a lap later.
Massa enjoyed a positive start to the race, leading Ferrari team-mate Fernando Alonso for many laps. But the Brazilian's second pit stop was tardy. Alonso remained out on track for six more laps, which meant that when he made his second stop he had less distance to run until the chequered flag so was able to fit soft rubber.
As Alonso exited the pits, however, he was level with Jean-Eric Vergne, who in turn was fending off Massa. The Spaniard had to drive off the track to stay ahead of both men, an incident that attracted the attention of the race stewards, although he was cleared of any wrongdoing after the race.
Massa ran wide off the track in ninth place, although he recovered to overtake Toro Rosso driver Vergne on the following lap. Revelling in the extra grip supplied by his fresh tyres, Alonso swooped ahead of Hamilton for sixth place, and then quickly dealt with di Resta for a provisional fifth on the road.
Hamilton had a relatively quiet race in which he struggled for grip and straight-line pace, leaving him unable to make much progress.
Di Resta's one-stop drive into the points was a masterclass in tyre conservation. His team-mate Adrian Sutil adopted a similar strategy, but faded near the end and was overtaken for ninth position by Sergio Perez on the final lap.
Perez's team-mate Jenson Button was one of a handful of drivers to take the tactical decision of starting the grand prix on the softer tyre compound, but any chance of earning points was stymied by contact in the opening corners that damaged his McLaren's front wing. He had to make an unscheduled pit stop for a replacement on lap two and failed to make significant progress after the delay.
Nico Hülkenberg ran brightly in the early stages of the race, but his day was ruined by a drive-through penalty for an unsafe release from the pits after a tyre change.
Kimi Räikkönen had a torrid weekend, which started with him threatening to go on strike, citing alleged non-payments by his Lotus team. After he had qualified fifth on the grid on Saturday, he was excluded from qualifying when scrutineers found a technical irregularity with his car. His race ended at the first corner, where he clashed with one of the Caterhams and inflicted terminal suspension damage on his car. The Finn left the circuit before the race had reached the half-distance point.
After the race, Vettel stopped the car off the circuit and delighted the crowd with some more doughnuts in his Red Bull; the same antic that earned him a fine and a reprimand at the previous race. This time, however, team boss Christian Horner insisted that the world champion pay the fine that was sure to come their way, rather than the team pick up the tab.
The German equalled the record of seven straight wins set by his compatriot Michael Schumacher in 2004. Ascari actually won nine times in as many starts across the 1952/53 seasons, but in the midst of that run he and Scuderia Ferrari skipped the Indianapolis 500. The American classic was a counting round of the world championship in those days, albeit one rarely contested by the regular grand prix teams.
Abu Dhabi Grand Prix, 3 November 2013, round 17/19
1 Sebastian Vettel (Red Bull)
2 Mark Webber (Red Bull)
3 Nico Rosberg (Mercedes)
4 Romain Grosjean (Lotus)
5 Fernando Alonso (Ferrari)
6 Paul di Resta (Force India)
7 Lewis Hamilton (Mercedes)
8 Felipe Massa (Ferrari)
9 Sergio Perez (McLaren)
10 Adrian Sutil (Force India)