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It's also the first of a quickfire double-header, as the two clubs meet again in the Premier League at St James' Park just four days later.
Everton's season started brightly with an eight-match unbeaten run, but they've since lost back-to-back league games 2-0 to Chelsea and Arsenal, and they've scored fewer goals than all but the three sides in the relegation zone.
A cup run would be a welcome tonic for David Moyes, with the club's last trophy dating back to the 1994/95 FA Cup.
The Toffees have seen off Preston (4-0 away) and Wolves (1-0) so far, and they're looking to reach the last eight for just the second time in six years.
Newcastle, by contrast, have serious pedigree in this competition. No side has won more EFL Cup ties than their 18 since the start of 2022/23, they've won each of their last seven fourth-round ties, and they're chasing a quarter-final place for a fifth year running.
Mattias Jaissle's side also arrive in better spirits after a 2-0 win at Crystal Palace eased the pressure that had been building on the new boss.
Everton vs Newcastle: Betting tips
• Under 3.5 goals - 2/5 with Bet365
• Over 8 corners - 4/6 with Bet365
• Thierno Barry to score or assist - 13/10 with Bet365
Odds courtesy of Bet365. Correct at the time of publication and subject to change.
Under 3.5 goals
Everton prioritise defensive solidity under Moyes, and five of their last six matches have featured fewer than 2.5 goals, which points towards a low-scoring cup tie.
Their attack has been the weak link recently, with back-to-back 2-0 defeats and a league goal tally that sits near the bottom of the table.
With the same two teams meeting again in the league four days later, neither manager has much incentive to throw caution to the wind, and Newcastle's last two wins, 1-0 at Millwall in the previous round and 2-0 at Palace, were both fairly controlled. At 2/5 with Bet365, Under 3.5 goals looks like a safe way in.
Bet explanation: This bet wins if the combined goal tally between Everton and Newcastle United is three or fewer after 90 minutes.
Over 8 corners
Newcastle are expected to name a relatively strong line-up again, as they have in the previous two rounds, and that attacking quality should see them spend plenty of time in Everton's half.
Against a compact home defence, they're likely to go wide and win set pieces rather than find easy routes through the middle.
Everton, meanwhile, will push for a breakthrough at home if they fall behind, and with a direct approach they should win some corners of their own. With the tie needing a winner, a high corner count looks probable, and Over 8 corners at 4/6 with Bet365 is worth considering.
Tip: Over 8 corners @ 4/6
Bet explanation: This bet wins if the combined number of corners taken by both teams is ten or more.
Barry to score or assist
Barry has been Everton's main attacking threat this season. Only Erling Haaland has had more shots in the Premier League, and the Everton striker has scored six goals in ten appearances, including a hat-trick in the round-two win at Preston.
With Everton's attack otherwise struggling for goals, much of their creative play runs through him, and he's expected to lead the line again on Thursday.
At 13/10 with Bet365, backing him to score or assist offers the best price on the card.
Tip: Thierno Barry to score or assist @ 13/10
Bet explanation: This bet wins if Thierno Barry scores a goal or provides an assist during the match.
Everton vs Newcastle: Betting odds
• Everton - 11/10 with Bet365
• Draw - 5/2 with Bet365
• Newcastle United - 21/10 with Bet365
Odds, correct at the time of publication, are subject to change.