Rogic was replaced after 58 minutes by Callum McGregor, after former Dundee United midfielder Armstrong had opened the scoring in the 39th minute to give an otherwise dull first half a notable end.
The champions came out flying at the start of the second half and notched two goals in a minute from Armstrong and returning striker Leigh Griffiths and although Jags defender Liam Lindsay reduced the deficit with a header just after the hour mark, McGregor restored their cushion for Brendan Rodgers's side who still have two games in hand over second-placed Rangers.
For a game that Celtic were odds-on to win, Rodgers made three changes to the side which started in the 1-1 UEFA Champions League draw with Manchester City in midweek.
Defender Cristian Gamboa, winger Gary Mackay-Steven and striker Griffiths came in for Jozo Simunovic, James Forrest and Moussa Dembele, the latter starting on the bench.
Attacker David Amoo and midfielder Chris Erskine returned to the Thistle line-up at the expense of Ade Azeez and Ryan Edwards, who were among the substitutes. Edwards, who had a spell on loan at Perth Glory in 2013–2014, came on in the 56th minute.
Thistle also looked solid enough defensively in the early stages although in the 23rd minute Jags keeper Tomas Cerny had to make a fine save from Griffiths's low drive after winger Patrick Roberts had set him up with a cut-back.
Moments later, the Scotland attacker drove wide from 25 years with an effort which was as unconvincing as the visitors' play.
The Maryhill men were even less potent.
Erskine's angled-drive from 16 yards in the 33rd minute flashed past Craig Gordon's far post with no real chance of beating the Celtic keeper before Cerny had to race outside his box to thwart Griffiths after he raced on to a Rogic throughball.
However, it was Griffiths who became provider in the 39th minute when he got past right-back Ziggy Gordon and drove the ball across the six-yard box and past Cerny for on-rushing midfielder Armstrong to slam into the net for his fifth of the season.
Armstrong's second four minutes after the restart was a finish of real quality as he accepted a free-kick from Griffiths before curling a left-footed shot from 25 yards past Cerny and into the far corner.
The visiting fans were still celebrating when Griffiths took a pass from Rogic, rolled Thistle defender Adam Barton with some ease before lifting his shot high into the net.
When Lindsay, making his 50th appearance for Thistle, looped a header from a Sean Welsh free-kick over Gordon, a comeback was hinted at and the Celtic fans in the 7,609 crowd revealed some relief moments later when Welsh's header from a Callum Booth free-kick which found the net was ruled offside.
As the Parkhead side reasserted themselves, Roberts fired over from close range, Cerny made a great save from Griffiths's close-range drive and Lindsay blocked a drive from Dembele, on for Roberts, for a corner which came to nothing.
In the 81st minute left-back Emilio Izaguirre reached the by-line before sitting his cross up for McGregor to volley in number four and keep Celtic unbeaten in the league - they have dropped two points - and inexorably on way to their sixth successive title.