Dibaba, 27, who won the distance double at the 2008 Beijing Olympics, saw off Sally Kipyego and Vivian Cheruiyot with a final-lap burst to win by more than five seconds.
Dibaba's time was a season's best 30:20.75, with Kipyego taking the silver in 30:26.37, and world champion Cheruiyot bronze in 30:30.44.
In the Shot Put competition, Germany's 22-year-old hopeful David Storl, the reigning world champion, had set the standard with a throw of 21.86m but Majewski responded to claim gold with 21.89m.
USA's Reese Hoffa failed to capitalise on his good form this season but still took bronze with his throw of 21.23m.
The prospect of records tumbling on the running track was reinforced by the heats for the women's 100m. No fewer than six women qualified for the semi-finals in under 11 seconds - in the past, the only other women to do that have gone on to win gold.
USA's Carmelita Jeter was fastest in 10.83, but her big rival Shelly-Ann Fraser-Pryce, from Jamaica, slowed down noticeably in winning her heat and still managed 11.0.
In the men's 1500m heats, Algeria's Taoufik Makhloufi ran the fastest time, 3:35.15, while Kenya's Asbel Kiprop, the defending champion who is aiming to emulate Sebastian Coe's back-to-back Olympic titles, was a comfortable third-fastest in 3:36.59.
Great Britain's Jessica Ennis turned a sensational start in the Heptathlon into a 184-point lead following the opening four events.
Ennis produced the fastest 100m hurdles ever run in a Heptathlon, clocking 12.54 to smash her personal best and break the GB record with a time which won individual gold at Beijing 2008.
A clearance of 1.86m in the high jump gave Ennis a 25-point lead after two events, before a world Heptathlon best of 17.31m in the shot from Austra Skujyte took the Lithuanian into a 64-point lead.
However, Ennis then set another personal best of 22.83 in the 200m for a total of 4,158 points, her best ever first-day score and enough for a lead of 184 points over Skujyte.