Porter appeared to be well offside as he helped David Clarkson's shot into the net in the 66th minute but the flag never came.
The English striker headed the opening goal of the Scottish Premier League clash from Bob Malcolm's dangerous free-kick in the latter stages of the first half.
There were angry scenes at the end of of the Lanarkshire derby as both management teams argued on the touchline.
Despite the disputed second, Motherwell were well worthy of a victory that took them to 16 points after the first round of games - the same amount as last season, when they went on to claim third place. And they returned to their best form under Mark McGhee's favoured 4-3-3 formation.
Former Motherwell pair Richard Offiong and Simon Mensing among were among five Hamilton players recalled following Tuesday's Co-operative Insurance Cup defeat at Rangers, but their losing streak increased to six matches.
Accies had held the bragging rights over their neighbours though following September's 2-1 League Cup win.
And Offiong carved out the first half-chance in the 10th minute when he collected Corcoran's low cross with his back to goal and shot from 12 yards, but Graeme Smith got down to save.
Porter went closer when his 18-yard drive was pushed just past by Tomas Cerny after the striker had created space with a clever dummy and taken John Sutton's return pass.
Offiong had a long-range drive held by Smith following more good wing play from Corcoran.
Motherwell were gradually getting on top and David Clarkson leapt well to win a Stevie Hammell corner, but his header struck Porter in the six-yard box as the ball appeared set for the far corner.
The big striker made amends in the 37th minute when he glanced home the opening goal following Bob Malcolm's free-kick.
The centre-back curled the ball goalwards from the left edge of the box and Porter got the slightest of touches to help it home.
Hamilton should have levelled four minutes before the break when Mensing drove forward and slipped the ball through for Corcoran, but he dragged wide from 12 yards with only Smith to beat.
Well continued to dominate after the break and Clarkson shot straight at Cerny after breaking with Marc Fitzpatrick.
Sutton shot two yards wide from 20 yards after linking well with Porter, and the pair combined again as Well hit the woodwork in the 53rd minute.
Sutton's cross from the right found Porter six yards out but his header bounced off the post and fell into Cerny's arms.
The hosts missed another great chance when Clarkson volleyed over the onrushing Cerny but wide after Sutton had headed on Smith's kick-out.
Hamilton needed a change and Billy Reid brought on James McCarthy and Stephen Ettien, who scored the extra-time winner in the cup.
McCarthy immediately made his mark by fouling Fitzpatrick, who appeared to kick out at the teenager, but it was James McArthur who was booked for his angry reaction.
Hamilton had a much bigger grievance as Porter doubled the lead with another deft touch.
The striker looked offside as he helped Clarkson's low drive into the net from inside the six-yard box and Cerny was booked as the protesting Hamilton players surrounded the assistant referee.
Jamie Murphy came off the bench and immediately had a chance for the third following a long ball but Cerny blocked his low drive with his legs.
Ettien created Hamilton's first chance of the half when he cut the ball back for David Elebert 15 yards out, but the defender shot into the sidenetting.
Hammell was booked for a bad foul on McCarthy, which sparked angry scenes on the touchline.
A police officer and fourth official Willie Collum stepped in between Reid and Motherwell assistant manager Scott Leitch as the Hamilton boss made for the home dugout.
Well retained the attacking edge and Porter forced Cerny to dive low to his right to prevent him bagging a hat-trick.
Mensing had a chance to spark a late fightback but he headed straight at Smith from 15 yards.
The final whistle saw a resumption of hostilities on the touchline as Motherwell boss Mark McGhee was pulled away by Leitch from a heated argument with the Hamilton contingent.