Ivorian forward Arouna Kone netted a clinical hat-trick as Everton demolished Sunderland 6-2 in the Premier League on Sunday, while Southampton overcame south-coast rivals Bournemouth 2-0. (Read more football stories here)
Sunderland had been buoyed by a 3-0 victory over derby rivals Newcastle United in their previous fixture, but despite hitting the post twice in the early stages and coming back from two goals down to make it 2-2, Sam Allardyce's struggling side were well beaten.
Goals by Jerman Defoe and Steven Fletcher allowed Sunderland to level after Gerard Deulofeu and Kone had put Everton 2-0 up, but a Sebastian Coates own goal and a Romelu Lukaku effort restored the hosts' control in the second half before Kone completed his treble.
Everton manager Roberto Martinez praised Kone for fighting back from a career-threatening knee injury sustained in 2013, saying: "His attitude, his focus never changed and he never chose to blame anyone and anything.
"He is a sensational example to any young footballer facing adversity."
Kone's performance had the added bonus of triggering an appearance clause in his contract that will see his deal automatically extended for a further 12 months at the end of the season.
His treble helped Everton score six goals in a league game for the first time since a 7-1 win over the same opponents in November 2007, as Martinez's side climbed to ninth place in the table.
Sunderland remain second from bottom, two points from safety, and new manager Allardyce, who switched to a three-man defence for the game, said his players had paid the price for a lack of positional discipline.
"We had 17 attempts on goal and 12 on target," he said.
"At the top end we can score a goal and create chances, but until we get into the habit of defending better out of possession, it is worthless how many goals we score if we defend like that."
At St Mary's, Steven Davis and Graziano Pelle scored neatly constructed first-half goals as Southampton beat local rivals Bournemouth to move up to seventh place, four points below the Champions League berths.
Davis volleyed in a cross from Ryan Bertrand in the 31st minute and Dusan Tadic teed up Pelle to head home five minutes later as Ronald Koeman's team extended their unbeaten run to five league games.
Southampton's Kenyan midfielder Victor Wanyama was sent off in the 78th minute after receiving a second yellow card for upending Lee Tomlin, but the 10 men emerged unscathed.
Eddie Howe's Bournemouth, beaten 5-1 by Tottenham Hotspur and Manchester City on their two previous league outings, remain a point above the bottom three in 17th place.