The new cinematic mode "anticipates when someone is about to enter the frame" and shifts focus to them, Apple said - something known as "pull focus".
It is the only smartphone that lets users edit this effect into videos after shooting, CEO Tim Cook said.
However, most other features on the new model were incremental updates over previous versions.
The event was also overshadowed by news of a new security flaw in Apple devices which could expose users' messages.
Apple released a security patch on Monday for the previously-unknown flaw, which could let attackers access its iMessage service without the user clicking on a malicious link or file.
The new iPhone includes a faster A15 chip, a brighter display, and a battery life of up to 2.5 hours longer, and comes in new colours including pink, blue, "midnight starlight" and red.
The new iPhone will also have up to 500GB of storage with its lowest available storage rising to 128GB from previous models' 64GB.
Apple was also keen to stress its green credentials. Kaiann Drance, VP iPhone product marketing, said the new model was "designed with environment in mind, using many recycled materials" - its antenna lines are made using upcycled plastic water bottles, an industry first, she said.
The new phone comes as buyers are keeping their phones for longer before upgrading. Investment firm Wedbush Securities estimates that around 250 million iPhone users have not upgraded their phones in 3.5 years.
"The iPhone remains a core lucrative product for Apple as it represents a gateway to other devices and more importantly services," said Paolo Pescatore, an analyst at PP Foresight.
"While many will see some upgrades as incremental, there are millions of users who have yet to upgrade to 5G. Therefore, this so called 'supercycle' moment is still relevant."
The 5G connectivity is only available on the iPhone 12, released last year, and the new models.
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In the second quarter of this year, Apple shipped 25.9% of all 5G handsets in the world, according to analyst firm IDC.
Marta Pinto, senior research manager at IDC, said: "With the new portfolio, this number will grow and consolidate the dominance of Apple in that space."
"Not being the first [to launch a 5G phone] paid off."
Apple also launched an iPhone 13 Mini, Pro and Pro Max. Ms Pinto said the slightly different models "shows that Apple knows the audience really well and is targeting different customers."
The iPhone 13 Pro and Pro Max contain three cameras and what Apple calls "its most advanced camera system yet".
Its premium models include a Super Retina XDR display and ProMotion - which delivers adaptive refresh rates of up to 120Hz.
This allows for smoother scrolling, animations, and gameplay.
The iPhone 13 mini starts at £679, with the iPhone 13 starting at £779. The iPhone 13 Pro starts at £949, and the larger Pro Max £1,049.
Apple Watch Series 7
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Apple also announced a new version of its wearable Apple Watch.
The Series 7 brings the first redesign to the Apple Watch since 2018, and will be slightly larger.
The new size can fit almost 50% more text on screen, and has a keyboard to input text. It is also dust-resistant for the first time.
But manufacture of the Apple Watch Series 7 could face production delays, reported Bloomberg, which may lead to supply constraints.
Apple said the new model would be available "later this fall", whereas the new iPad also announced today at its virtual event is available from next week.
Apple currently accounts for 47% of the global smartwatch market, according to research from CCS Insight.
The new Apple Watch iOS 8 will also be able to automatically detect bicycle rides, including e-bikes.
"At first glance the latest Apple Watch is another iterative update, but the larger screen allowing bigger virtual buttons and a full qwerty keyboard should certainly improve usability," Leo Gebbie, principal analyst at CCS Insight said.
"I'd expected to see a bump in battery life on the Apple Watch, as owners continue to clamour for smartwatches to last longer, but Apple has decided not to deviate from its 18-hour battery life. The faster charging will be welcomed, but for those wanting to track their sleep it would be far easier to offer a battery that lasts a couple of days.
"Despite these concerns, the Apple Watch continues to sell in record numbers and dominates the smartwatch market by a distance."
iPad updates
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Apple has also launched a new version of its entry-level iPad. Cook said its iPad sales had grown by 40% in the past year.
It will be powered by the A13 chip, with 20% faster performance from its previous iteration. Apple said this was up to "three times faster than the Chromebook".
Those cheap styles of laptop exploded in popularity last year as schools shut down during the pandemic.
The new iPad starts at $329 (£319) and has a discounted price of $299 for schools.
A new iPad mini was also launched, with USB-C functionality, Apple pencil support and no home button - using a lock button on the top for Touch ID instead. Prices start at £479.
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