Tom Williams hit back for Cardiff but an impressive opening half from Warriors was capped with some sublime skill from Errie Claassens sending Chris Pennell over for a 20-10 lead at the break.
The hosts hit back with a brace from Williams to complete his hat-trick, despite much debate over his second when it appeared Pennell had forced him into touch.
A hectic finale saw Ceri Sweeney slot a late penalty to look to win it for the hosts before Frost's dramatic intervention gave Warriors the win they fully deserved after dominating for spells.
In typical pre-season fashion, the performance was always going to be more important to Head Coach Richard Hill than the result and he would have been encouraged by the first outing of the campaign.
Warriors showed plenty of attacking flair and will feel they should have scored more points and turned territorial dominance and a catalogue of chances in the Welsh capital into a bigger margin of victory.
But, ultimately, the rust was blown away over 80 minutes of hard graft and Hill will now look for his troops to up their performance levels when more Welsh opposition, in the form of Scarlets, visit Sixways next Saturday.
Blues, under the guidance of former Worcester coach Phil Davies, got the game underway and were on the front foot immediately as they looked to stretch Warriors before Macauley Cook made a line break and won a penalty that Tovey nudged over.
Warriors had the chance to respond within seconds as clear obstruction from the restart gave Goode a simple kick that he drove over to level the scores.
Worcester were looking lively in the opening exchanges as Aleki Lutui broke down the middle while Ravai Fatiaki introduced himself to the opposition with a typical huge hit in midfield.
A booming kick from Pennell forced Cardiff back and when Jon Clarke charged down a kick the alarm bells were ringing for Blues. A big visiting scrum then saw the ball shunted wide to young wing Ben Howard who was narrowly pushed into touch as he went for the corner.
Next to break away was Goode who then capitalised on his fine work by lining up a long range kick from just inside the Cardiff half that he crunched over to secure a 6-3 lead.
Slick hands from Lutui, Percival and Schofield then took Warriors up to the line before Perry and Claassens nearly combined to send the scrum half over as he just lost control of the ball.
The pressure was mounting and finally paid off with a scrum penalty close to Cardiff line, after big hit from powerful visiting pack. A huge shunt from the driving lineout saw Taulava crash over and Goode's conversion sent Warriors 13-3 clear.
With the Cardiff lineout failing time and time again, the game was being played predominantly in the home half before a sucker punch from the hosts of the half hour mark.
Howard just failed to take pass as Worcester looked to play from deep and Blues swooped to break down left at pace to send Williams over. Tovey added extras to reduce the lead to 10-13.
The visitors response was immediate and clinical as the impressive Taulava again made yards down the middle and took several men to haul him down.
After battering the short side, Worcester went left with a real injection of pace as Fatiaki floated a long pass to Claassens. The wing still had much to do, but je stepped inside the tackle and brilliantly offloaded to Pennell to score. Goode added the extras for a 20-10 half-time lead.
Worcester were denied what looked a good try just minutes after the restart as Claassens broke down the left and went for the corner only to be denied by the touch judge's flag after referee Gwyn Morris initially awarded the score.
Minutes later, on the opposite side of the pitch, Williams went for the corner after a flat pass sent him into space, but this time he was pushed into the sidelines by the covering tackle of Howard.
Williams, though, made amends on 50 minutes when an overlap saw him just about dot the ball down despite the attentions of Pennell who again clearly felt he had put him in touch with a last ditch tackle.
A searing break from Howard saw him make 40 metres, but fail to find supporting runners on his shoulder, while Matavesi showcased some amazing handling with an offload to Claassens round the back.
Worcester made a raft of changes just after the hour and Joe Carlisle almost made a huge impact as he sent Matavesi away down the middle and he threw a long pass out to Alex Grove who was just snagged short of the line.
Williams secured his hat-trick as he picked off Carlisle's long pass wide to sprint 80 metres unopposed and score with fly half Sweeney added the extras for a 22-20 lead.
The lead, though, lasted just moments as a penalty saw Carlisle drill over three points before a long spell of Worcester pressure came to no avail as a knock on saw the visitors lose the ball in the shadow of the posts.
A tense final few minutes ensued as both teams looked for the knock-out blow as Carlisle saw a long range penalty drop short before Pennell carved his a way through but failed to find Claassens with the final killer pass.
Cardiff mounted one last attack and looked like they secured the win when Sweeney knocked over a long range penalty.
But Warriors were not to be denied and the forwards drove up close with Chris Jones nearly stretching over before the ever-alert Frost picked up and dived over to a huge ovation from the visiting fans. Carlisle added the extras as Worcester opened with a morale boosting win.
02m Tovey p 3-0
04m Goode p 3-3
16m Goode p 3-6
19m Taulava t Goode c 3-13
31m Williams t Tovey c 10-13
33m Pennell t Goode c 10-20
50m Williams t 15-20
67m Williams t Sweeney c 22-20
68m Carlisle p 22-23
79m Sweeney p 25-23
80m Frost t Carlisle c 25-30
Warriors: 01 Ceri Jones (Mullan 39-40, 62), 02 Aleki Lutui (Hayes 62), 03 James Currie, 04 Dean Schofield (Percival 76), 05 James Percival (Gillies 62), 06 Chris Jones, 07 Sam Betty, 08 Semisi Taulava (Cowan 62), 09 Shaun Perry (Frost 62), 10 Andy Goode (Carlisle 60), 11 Ben Howard (Nellany 68), 12 Ravai Fatiaki (Matavesi 43), 13 Jon Clarke (Grove 62), 14 Errie Claassens, 15 Chris Pennell
Replacements: 16 Ollie Hayes, 17 Matt Mullan, 18 Ryan Furniss, 19 Craig Gillies, 20 Blair Cowan, 21 Ollie Frost, 22 Joe Carlisle, 23 Josh Matavesi, 24 Alex Grove, 25 Joe Nellany