The 21-year-old struck either side of efforts from Jude Bellingham and Raheem Sterling in a dominant first half before doubling his tally in the second, where substitutes Marcus Rashford and Jack Grealish also got in on the act.
Mehdi Taremi fired home two consolations for Iran, who were otherwise comprehensively beaten by Gareth Southgate's effervescent team as those in white kicked off their bid for glory in near perfect-fashion.
An issue with FIFA's ticketing app meant that a large number of fans could not take their seats in time for the national anthems, where Iranian players refused to sing in a show of solidarity with those protesting against the country's government.
Within just four minutes of the first half, controversy arose when Harry Maguire was hauled down by Roozbeh Cheshmi inside the area, but the officials did not deem anything to be wrong with the challenge.
Southgate's side continued to ramp up the pressure, but their momentum was halted in the seventh minute when Iran goalkeeper Alireza Beiranvand suffered a nasty clash of faces with Majid Hosseini, the latter of whom came away unscathed.
However, Beiranvand received treatment for several minutes as the Iran medical team tried to stem the flow of blood from his nose, but he was inexplicably given the green light to carry on after a lengthy delay.
Beiranvand lasted barely a minute before signalling to come off as Hossein Hosseini was introduced, and he remained relatively untroubled up to the half-hour mark.
Maguire crashed a header against the bar in the 32nd minute, but another Three Lions representative in Bellingham would get his header right three minutes later, meeting Luke Shaw's cross and directing a floating effort into the corner of the net for his first England goal.
The floodgates well and truly opened for England after Bellingham's opener, and Saka got in on the act in the 43rd minute, with Maguire heading down a corner for the Arsenal man to fire home on the half-volley with the help of a slight deflection.
Iran protests for a foul by Maguire did not bear fruit, and it was three for England at the start of a 14-minute injury-time period, as Harry Kane got away down the right and crossed for Sterling to volley home from close range.
Team Melli's best chance of the first half came when Alireza Jahanbakhsh volleyed harmlessly over the bar in acres of space late on, and Carlos Queiroz responded with a triple half-time substitution.
England were the victims of a few rough and late challenges from Iran early in the second half and came under a tad more pressure from Queiroz's men in their defensive third, but Jordan Pickford continued to receive adequate protection.
The Three Lions remained a constant threat going forward, and Saka would make it two for himself in the 62nd minute, cutting in from the right and opening up space inside the box before his low deflected effort found the bottom corner.
Iran would pull one back only three minutes later as Taremi lashed home off the crossbar following a smart pass from Ali Gholizadeh, before Southgate made four changes, including a withdrawal for Maguire after another concussion scare.
One of the newly-introduced substitutes - Rashford - would need just three touches to add to England's lead, cutting onto his left foot inside the box before calmly slotting home in the 71st minute.
With the game slowing down into the dying embers, there was time for England to add a sixth, as Callum Wilson burst down the right before picking out Grealish in the box for a simple tap-in on the 89-minute mark.
Following 14 minutes of stoppage time in the first half, another 10 were added on at the end of the second - the eighth minute of which forced Pickford to tip a close-range effort from Sardar Azmoun onto the crossbar and over the top.
However, hopes of England equalling their 6-1 thumping of Panama from 2018 were dashed when Iran were awarded a last-minute penalty by VAR, with John Stones tugging Morteza Pouraliganji down by the shirt, and Taremi sent Pickford the wrong way.
Wales and the USA will complete matchday one of Group B this evening before England meet the latter on Friday, while Iran will aim to recover from Monday's loss in their clash with the Dragons in four days' time.