The former Liverpool and Blackpool striker had made his debut as a second-half substitute in Thistle’s 2-1 Premiership defeat to St Mirren at Firhill on Friday.
The 23-year-old was keen to avenge that loss and the Jags did so thanks to his goal in the 10th minute of extra-time when he slotted into an empty net after Buddies goalkeeper Marian Kello had saved Christie Elliott’s initial shot.
The game had looked destined for extra-time following a first half that saw just two chances of note.
Kris Doolan was handed the first opportunity inside two minutes following good touches from Steven Lawless and James Craigen – but he curled wide from 16 yards.
St Mirren, who were missing Ellis Plummer to injury, also lost Gary Teale in the 26th minute after he came off worse in a shoulder charge with Jake Carroll.
Thistle were looking sharper in possession but any promising move broke down outside the penalty box and Saints had a half-chance to snatch an interval lead.
Gregg Wylde’s cross found Kenny McLean’s untracked run with home goalkeeper Scott Fox off his line, but the midfielder glanced his header wide.
The game immediately opened up after the restart and Kello palmed away Conrad Balatoni’s header after Craigen had crossed following a short corner.
Thistle were moving the ball much quicker and they kept the pressure on with Carroll fizzing a shot wide.
McLean headed wide again, this time following a deep corner, but Saints found themselves in trouble after another corner was cleared.
Lawless set substitute Ryan Stevenson away with an excellent first-time pass but he shot straight at Kello from 25 yards when he had support arriving to his left.
Saints had two great chances as the game entered the final 15 minutes.
Thistle put themselves under pressure with some sloppy defending and visiting right-back Adam Drury burst forward and fired a cutback that found Tom Reilly in space, but the striker’s shot was palmed wide by Scott Fox.
Reilly took the resulting corner and presented McLean with a free header but he again headed just wide with his best chance so far.
Thistle looked the much likelier team in the closing stages of the 90 minutes though – but Stuart Bannigan and Lawless both missed the target when loose balls fell for them 18 yards out and Kallum Higginbotham shot against a team-mate after Lawless had cut the ball back to him.
Saints sub James Marwood had the first chance of extra-time but Fox comfortably saved and Saints were undone when they failed to pick up Lawless in the centre circle and were put on the back foot.
Eccleston finished off the move and Fox saved comfortably from Reilly, and McLean’s 60-yard shot, to send Thistle through.