After they had resisted much of the hosts' pressure, Arter struck well over the crossbar when he could have secured all three points and further eased the fading threat of relegation.
A draw instead leaves Bournemouth 11th in the Premier League and level on 34 points with their 10th-placed rivals, who have two games in hand. They also sit seven points clear of the bottom three.
Following a week in which Southampton's Dusan Tadic had complained about the frequency with which Claude Puel substitutes him and his manager had responded by telling him to respond on the pitch, the midfielder was gifted the game's first chance.
He found himself with time and space to run into at the edge of the area in the fourth minute, but despite being well positioned the Serbian sent his left-footed shot both high and wide.
Bournemouth's Dan Gosling shot over the crossbar from similar territory in the 29th minute after goalkeeper Fraser Forster's unconvincing punched clearance.
Shortly afterwards, Southampton's Steven Davis was then forced into clearing off the line after Andrew Surman touched Ryan Fraser's right-wing corner beyond Forster, and from that point each team provided a regular threat.
Typically promising build-up play on the right wing between James Ward-Prowse and Cedric created space for the latter to cross to Tadic, and after Jay Rodriguez dummied, the midfielder curled just wide of the left post.
Tadic then played a classy ball over the top of Bournemouth's defence towards Rodriguez, from where the forward took advantage of the kind bounce to shoot towards the top right corner. The diving Artur Boruc tipped the ball away.
Read the full article on eurosport.co.uk: Arter fluffs penalty chance as Bournemouth draw at Southampton