Dorset Police arrested seven Newcastle supporters, including a 14-year-old, as trouble flared during the Premier League game at Bournemouth.
Visiting fans spilled on to the Vitality Stadium pitch while celebrating Matt Ritchie's stoppage-time equaliser which rescued a 2-2 draw for Newcastle.
Salomon Rondon gave Newcastle the lead before Bournemouth's Josh King scored from the penalty spot, and then grabbed his second nine minutes from time.
However, Ritchie's stunning volley in injury-time snatched Newcastle a late point, and sparked ugly scenes as some visiting fans entered the pitch and clashed with stewards.
A possible assault on a female steward, who suffered an injury to her nose, is also being investigated.
"Six men and a 14-year-old boy were arrested on suspicion of going onto the playing area at a football match from the away supporters' stand and are assisting officers with their inquiries," read a statement from Dorset Police.
"One female steward sustained an injury to her nose during the incident and investigations are under way to establish whether any assault took place."
Trouble caused by supporters entering the field of play has been in the spotlight following a series of high-profile incidents last weekend.
Birmingham supporter Paul Mitchell was jailed after punching Aston Villa midfielder Jack Grealish in last Sunday's second city derby, while Manchester United defender Chris Smalling appeared to be pushed by an Arsenal fan on the same day.
Those events followed Rangers captain James Tavernier being confronted by a pitch invader at Hibernian two days earlier.