Tunji Akinola put the Jags in front after 12 minutes, but it wasn’t until the second minute of stoppage time that fellow centre-half Kevin Holt put the tie beyond hosts Stranraer with a second goal.
Thistle gaffer Ian McCall conceded that the League 2 hosts had made it difficult for his side, currently second in the Championship.
He told the club website ptfc.co.uk : “It’s good to get the win first and foremost and I was really happy with the first half performance.
"We were well on top and should have scored a couple more at least but at the end of the day we’re through and that’s what it’s all about in cup football.
“We used the wide areas well in the first half and created some really good chances but just weren’t ruthless enough when in front of goal and with the score at 1-0 it was still game on going into the second half.
"They made it a real cup tie in the second half and it became a bit end-to-end at times. We stood up well to that though and Jamie didn’t need to make all that many saves overall. Tunji and Kevin looked very good together again, winning headers and making blocks so I was happy with how we dealt with what Stranraer threw at us.”
Thistle now face Queen of the South away in the next round, the tie scheduled to be played on Saturday, October 9.
This Saturday they head north for a top-of-the-table clash with leaders Inverness Caley Thistle.