Substitute Goode's appearance for the second half heralded a stirring Warriors fightback after they trailed 10-6 at half-time.
Goode, though, wiped out that deficit within six minutes of arriving off the bench when he converted his own try to follow a couple of earlier Joe Carlisle penalties.
Goode then added a penalty of his own before ex-Gloucester wing Marcel Garvey sprinted 80 metres for a clinching touchdown after the Warriors soaked up sustained pressure.
Miles too good: Worcester's Miles Benjamin breaks the tackle of Olly Morgan
Gloucester, who saw full-back Olly Morgan carried off injured early in the second half, claimed a 25th-minute try through wing Charlie Sharples, while fly-half Freddie Burns added a conversion and penalty.
But they were ultimately undone by Worcester's ferocious commitment, especially in defence, despite Jonny May's consolation touchdown that secured a losing bonus point.
On a day when several players looked to leave final impressions on interim England coach Stuart Lancaster ahead of his 32-man elite squad announcement next Wednesday, it was 31-year-old Goode who stole the show.
And it means Worcester will head into a five-week break from league action with successive league wins under their belt and climbing towards mid-table status, well clear of bottom club Newcastle.
Warriors boss Richard Hill recalled prop Tevita Taumoepeau and flanker Jake Abbott following last weekend's 6-0 win at Wasps, which opened up a 10-point gap between Worcester and Newcastle.
Gloucester, meanwhile, welcomed back former England lock Alex Brown from a long-term injury as the only change following a 15-15 draw away to Premiership champions Saracens last time out.
Brought back down to earth: Mike Tindall is tackled
The visitors had recorded a solitary victory from their last 10 league away games, but they started brightly as Burns booted them a 12th-minute lead.
Although his opposite number Carlisle quickly cancelled out that strike, Worcester's attacking failings - just nine tries in 12 Premiership matches this season - soon surfaced.
Wing Miles Benjamin, who has been linked with a move to Leicester next season, should have been freed on more than occasion, but the final pass proved Warriors' undoing.
Gloucester absorbed considerable pressure before establishing a strong territorial position and executing a well-worked try when Morgan and centre Henry Trinder combined to send Sharples scurrying over.
Referee Martin Fox required confirmation from the television match official before awarding Gloucester their opening touchdown, then Burns - who kicked five penalties in last weekend's draw against Premiership champions Saracens - added a testing touchline conversion.
It was a vivid lesson to Worcester on how to create and take chances, yet they did not learn their lesson and scrum-half Jonny Arr was guilty of blowing a golden opportunity just before half-time when he spilled possession in open play.
Carlisle reduced Warriors' arrears through a second penalty with the opening period's final kick, but Gloucester were good value for their lead, even if a 10-6 advantage meant they still had plenty of work to do.
Warrior sandwich: James Simpson-Daniel struggles to beat the Worcester defence
Carlisle was replaced following an indifferent first half display, and it took Goode little time to make his mark on a game that saw Worcester requiring inspiration.
The ex-international No 10 had an immediate penalty chance, but after that bounced back off post, Worcester retained attacking momentum.
And Gloucester were then powerless to prevent Goode from scoring between the posts, with his conversion putting Warriors 13-10 ahead, before a penalty extended that advantage by a further three points.
Gloucester, in the meantime, saw Morgan carried off, and then Worcester struck a killer blow after some fearless defending kept their opponents at bay.
Trinder tried to break down the Warriors with a kick into space inside Worcester's 22, but Garvey gathered a kind bounce and then surged away up field without a Gloucester player touching him.
Goode missed the conversion and a later long-range penalty attempt, yet Worcester were home and dry, claiming a derby victory to savour despite May's late effort and celebrating first back-to-back Premiership triumphs since April 2009.