The opener came after 17 minutes when Storer picked up a headed clearance from Michael Tidser and cracked a half-volley past Ryan Scully from 25 yards.
The lead was doubled on 29 minutes when Penrice slammed home a Chris Erskine cross with former Greenock favourite Thomas O’Ware heading against the post shortly afterwards as Thistle looked to put the game to bed.
Early in the second half Tidser saw a shot deflected wide and Jack Iredale was denied by Cammy Bell as Morton looked to get back into things.
Debutant Tumilty, who had only joined the Greenock men yesterday, grabbed a goal with a well-struck shot 16 minutes from time with Jack Purdue going closest to a leveller.
In the other game in Group E, Stenhousemuir defeated Albion Rovers 4-0 thanks to goals by Morgyn Neill, Connor Duthie, Sebastian Ross and Sean Dickson.
Neill nodded the opener on 54 minutes and, two minutes later Duthie drilled in with Ross volleying home before Dickson completed the scoring in injury time.
Montrose top Group B after defeating East Fife 1-0 with Danny Cavanagh hitting the winning goal on 56 minutes. Falkirk are second after they won 2-0 against a Forfar side who should have been winning at the break. The visitors’ Jamie Bain had an early penalty saved and team-mate Thomas Reilly shot against the post twice before half-time.
Dennon Lewis opened the scoring on 54 minutes with Deimantas Petravicius firing home the second eight minutes from time.
Inverness Caledonian Thistle survived a scare at Cowdenbeath before winning 5-2 to top Group C.
The Blue Brazil’s Jordyn Sheerin drilled in from 25 yards to grab his third goal of the tournament midway through the first half with Tom Walsh restoring parity from the edge of the box ten minutes from the break.
Walsh added a solo effort on 41 minutes with Aaron Doran poking in the third before half-time.
George Oakley added a fourth on 73 minutes after Jordan White had been denied. Before the end Doran grabbed his second and Sheerin did likewise for the hosts.
In Group D Dunfermline enjoyed a 3-0 win over visitors Peterhead with debutant Myles Hippolyte heading in on 41 minutes. Kallum Higginbotham added the second from the penalty spot two minutes from time and Andy Ryan grabbed an injury-time third.
Callum Tapping struck from 20 yards to earn Brechin their first win of 2018 with a 2-1 success at Stirling Albion. Bruno Melingui nipped in behind the home defence on 17 minutes to open the scoring, but Mark Stewart slotted in for the hosts right on half-time to level before Tapping struck six minutes from time.
Queen of South saw off Clyde 3-0 at Palmerston in Group G with Stephen Dobbie, pictured, grabbing a second-half hat-trick.
The hitman notched the opener on 47 minutes and two minutes later Dobbie cracked in before slotting home the third 12 minutes from time.
Alloa’s first game in Group A ended in a 4-2 win over visitors Arbroath with all six goals scored in the first 36 minutes
The Wasps’ Greig Spence opened the scoring on nine minutes and Kevin Cawley’s deflected effort 60 seconds later doubled their advantage.
Ryan Wallace pulled a goal back on 20 minutes from close range and Kane Hester levelled on 26 minutes when he slid the ball into the empty net.
Alan Trouten hit the post before knocking the rebound in to make it 3-2 with Spence curling in his second to end a goal-laden period.
Dumbarton defeated a dogged Queen’s Park side 1-0 in Group H, the winner coming on 35 minutes through Calum Gallagher.
Annan top Group F ahead of Hamilton and Livingston after a 4-0 home success over Berwick Rangers.
Tommy Muir grabbed a first-half double, David Wilson’s fierce shot making it three before Scott Roberts added the fourth on 52 minutes.