Arne Slot's team temporarily moved to the top of the Premier League table with the victory over the Cherries, but faced an early scare when Antoine Semenyo had a goal disallowed for offside.
After regaining their composure, the hosts surged ahead to a 3-0 lead within 40 minutes, thanks to a brace from Diaz and a superb curling strike from Darwin Nunez.
The goal by Nunez was his first for the Reds since early April, though he was on target for Uruguay at the Copa America over the summer.
Alexander-Arnold notches up Liverpool record
Alexander-Arnold's assist for Diaz's second goal of the afternoon meant that the England right-back has now reached 100 goal involvements for Liverpool.
It was also his second assist in as many games after he laid on Ibrahima Konate's goal against AC Milan in the Champions League on Tuesday night.
The 25-year-old achieved the remarkable feat in his 316th competitive appearance for the Reds, and his century of goal contributions have come via 19 goals and 81 assists.
A total of 74 goal involvements have come in the Premier League, including scoring 15 himself and setting up a further 59.
Additionally, he has contributed to 15 goals in the Champions League and two from five appearances in last season's Europa League, while the remainder have come in the FA Cup, EFL Cup and Community Shield.
Alexander-Arnold's sensational stats at Liverpool
Since making his competitive debut for Liverpool in 2016 against Tottenham in the League Cup, Alexander-Arnold's 81 assists rank as the third most by any Premier League player in all competitions, trailing only Kevin De Bruyne (146) and teammate Mohamed Salah (92).
Salah, who also picked up an assist in the win on Saturday, is one of only three players to have more goal involvements for Liverpool than the England international since the 2016-17 season, alongside Roberto Firmino (100 goals and 62 assists) and Sadio Mane (120 goals and 37 assists).
By achieving this milestone at the age of 25 years and 350 days, Alexander-Arnold became the youngest player to record 100 combined goals and assists since Steven Gerrard, who reached the mark at 25 years and 72 days in August 2005.
His most productive season with Liverpool was in 2021-22, during which he played a role in 20 goals across all competitions, including scoring two assisting 18, surpassing his 19 contributions from the 2019-20 season when they clinched the Premier League title.