A match pitting together two of the Premier League's mid-table clubs never looked likely to provide a feast of entertainment and the visitors' lack of ambition made for a largely drab affair, until a frantic final 30 minutes in which Wayne Rooney missed a penalty and Anthony Knockaert saw red.
Sam Allardyce's side certainly showed more desire to force the issue and were left to dwell on a first half of missed chances after going in goalless at the break.
But Bong inadvertently made the breakthrough in the second half when he shinned Yannick Bolasie's curling delivery into an unguarded net, with Theo Walcott lurking.
Tosun then scored for the second game running as he fired in off the underside of the crossbar and Knockaert was dismissed for the Seagulls having lunged in on the returning Leighton Baines, before Mat Ryan made an excellent save from Rooney's spot-kick.
The Toffees have now lost just once in 10 home league matches since Ronald Koeman left, with Saturday's triumph all but securing their top-flight safety.
Brighton can also almost begin to plan for another campaign among the elite, despite having seen a fine seven-match unbeaten streak in all competitions ended in meek fashion.
Everton (@Everton) March 10, 2018
Baines' return to action for the first time since November headlined Everton's four changes and Allardyce's men – beaten 2-1 at Burnley last time out – showed some positive early intent.
Seamus Coleman dragged a low shot beyond the far post in a dominant start for the hosts, who also saw Bolasie prod wide on the volley after Ryan had flapped at a cross.
Brighton's first shot came in the 25th minute as Glenn Murray stung the palms of Jordan Pickford from 25 yards, sending a timely reminder of the visitors' potential threat.
Bolasie did well to get behind the Albion defence and connect with a looping header that dropped narrowly off target, with Ryan's goal living a somewhat charmed life.
A low-key start to the second half saw the Goodison crowd fall into near silence until Rooney's thunderous drive was bravely blocked away by Shane Duffy.
And the breakthrough arrived on the hour mark, Walcott seeking to latch on to Bolasie's deep cross and Bong diverting into his own net under pressure.
Chris Hughton's charges, winless away from home in the league since November, struggled to mount any meaningful response against a home side who lost Walcott to injury 18 minutes from time.
Everton shrugged off that setback as Baines fed Tosun, who produced a powerful finish that rattled in off Ryan's crossbar.
There was still time for Knockaert to see red following a moment of madness in which he dived in two-footed on Baines, while Rooney spurned the chance to increase the margin of victory after Dominic Calvert-Lewin had been fouled by Duffy.
Key Opta facts:
- Everton have lost only one of their 10 previous league meetings with Brighton and Hove Albion (W5 D4).
- The Toffees have won seven consecutive Premier League home games against newly promoted sides for the first time in the competition.
- Brighton's 2-0 defeat to the Toffees ended a five-game unbeaten run for the Seagulls in the Premier League.
- Brighton were the 41st different opponent Sam Allardyce has faced in the Premier League, while Derby County remain the only side he has failed to beat in England's top-flight (P4 W0 D1 L3).
- The Toffees kept their first Premier League clean sheet since Boxing Day – ending a nine-game run without a shutout.