Arsenal, West Ham and Aston Villa redressed the balance for Premier League teams after a flow of upsets in the FA Cup, securing narrow wins over awkward lower-league opposition to advance to the fifth round on Sunday.
Chelsea and Manchester City were among five teams in the Premier League's top nine to be eliminated on Saturday on one of the most astonishing days in the famous competition's history.
Senegal striker Diafra Sakho came off the bench and scored an 81st-minute header to earn West Ham a 1-0 victory at Bristol City, which is second in English football's third tier.
Villa had the toughest assignment against second-tier leader Bournemouth but came through with a 2-1 home win, with new signing Carles Gil — with his first goal since moving from Valencia — and Andreas Weimann scoring for the Premier League side.
Arsenal, which is fifth in the Premier League, is the highest-ranked team guaranteed a spot in the last 16 as Arsene Wenger's side looks to defend its title.
Walcott put Arsenal ahead in the second minute before Ozil, making his first start since October because of injury, was found by a probing pass from Tomas Rosicky and placed a finish into the corner.
Sloppy defending allowed Brighton to reduce the deficit through Chris O'Grady in the 50th but Rosicky restored Arsenal's two-goal lead by volleying in from the edge of the area. Sam Baldock lifted a neat finish over Arsenal goalkeeper Wojciech Szczesny in the 75th to set up a tense finish at the Amex Stadium.
West Ham toiled in the first half at Ashton Gate, clearing two headed attempts off the line, but improved after the break. Sakho, who entered as a 57th-minute substitute, struck the bar with a fierce shot before meeting Andy Carroll's cross with a far-post header from close range.
"Bearing in mind what has happened this weekend, it is a big result for us," West Ham manager Sam Allardyce said.
With Villa struggling in the Premier League and Bournemouth flying in the League Championship, their matchup had all the ingredients of another cup upset and the visitors had Villa at full stretch for much of the game.
However, Villa was clinical in front of goal, surprisingly given it is the lowest-scoring team in all four divisions in England, and Gil broke the deadlock by finding the top corner from 25 meters in the 51st.
Weimann's steered home Alan Hutton's cross to make it 2-0 in the 71st before Callum Wilson's injury-time response for Bournemouth.
It completed a positive day for Villa, with the club announcing that star midfielder Fabian Delph has signed a new 4½-year contract.
The draw for the fifth round is on Monday.
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