Liverpool and Chelsea were also able to secure wins, which will see both sides join the Hammers and the Magpies in the next round.
Click the links below to get all of our statistics from the respective matches.
West Ham 3-1 Arsenal
The Gunners appeared to have the better of the Hammers in the early stages, until Ben White turned the ball into his own net.
Continuing their fortunes in the second period, and seemingly growing in confidence, West Ham doubled their lead through new signing Mohammed Kudus - before Jarrod Bowen put the icing on the cake at 3-0.
Arsenal captain Martin Odegaard was only able to bag a late consolation goal away from home.
Bournemouth 1-2 Liverpool
The Reds dominated their hosts in the first period, but the resilient Cherries defended well in the early stages - until Cody Gakpo broke the deadlock after 30 minutes.
Bournemouth got themselves back into the tie in the second period, with a well-worked Justin Kluivert goal to make it 1-1.
But their hopes would be dashed pretty quickly as Darwin Nunez found the back of the net just five minutes after the equaliser.
Chelsea 2-0 Blackburn
There was an apparent gulf in ability at Stamford Bridge on Monday night, with the 2-0 scoreline perhaps flattering Rovers.
The Blues took a short while to get going, though - taking the lead through Benoit Badiashile after half an hour.
As is often the case with rotated squads, Chelsea grew in confidence as the match went on, and put the tie to bed in the second period through Raheem Sterling.
Man Utd 0-3 Newcastle
An evening to forget for the hosts, but what a result for the Magpies at Old Trafford.
The Red Devils never looked like scoring in the first period, which was capitalised on by Newcastle - scoring twice through Miguel Almiron and Lewis Hall in fairly quick succession.
Man Utd's players pushed themselves into a higher gear in the second half, but it was proven to be in vain after Joelinton put his side three ahead.
