Armstrong's thirteenth strike of the season saw Town gain an early advantage but they were pegged back when Rhys Hughes's free-kick found its way in the back of the net off Mark Oxley shortly before the break.
Both sides had opportunities and good spells of pressure, particularly after the break, but had to settle for a point apiece which inches Town further clear of the relegation spots.
Simon Weaver named an unchanged line-up to the side that defeated Barrow 1-0 a fortnight ago.
For the hosts ‘keeper Joe Murphy missed out through injury which meant that Mateusz Hewelt made his first start since Valentines Day.
And Hewelt's first action of the evening was to pick the ball out of the net when Armstrong delivered the perfect start after just three minutes. With time and space on the right-hand side George Thomson whipped in a dangerous cross that Town's top scorer steered home.
Armstrong would then turn provider on the quarter-hour mark when he swung across a tempting ball that only just evaded Danny Grant who was lurking at the far post.
From a Town corner Rovers staged a quick breakaway that almost caught the defence out, but a poor ball from Josh Hawkes allowed Tom Eastman the chance to easily recover the danger.
Armstrong had a golden opportunity just before the half-hour mark when Matty Foulds' long ball caught out Tom Davies. Armstrong controlled well, but frustratingly the ball then ran away from him as he prepared to shoot and his effort was ultimately blocked.
Rovers had a half-chance shortly after when Harvey Saunders found himself in space at the back post but his header was well wide of Mark Oxley's goal.
Anthony O'Connor went into the book ten minutes before the break when he hauled down Saunders after misjudging a through-ball aimed beyond the Town defence for the Rovers forward.
And from the resulting free-kick Hughes levelled matters after his free-kick struck the post and deflected back in off the back of Oxley.
Tails up, Rovers almost grabbed the lead a minute later when Josh Dacres-Cogley flashed a ball across the six-yard box that Town scrambled clear.
O'Connor then headed behind from under his own bar under heavy pressure from Joel Mumbongo with Town relieved to get through to the break with no further pressure on their goal.
After being under heavy pressure at the end of the first-half Town came out firing after the break. A couple of minutes into the half Kazeem Olaigbe forced Hewelt into a low save down to his right but they were soon on the back foot again.
Josh Falkingham went into the book after conceding a free-kick in a dangerous position, which was cleverly taken to Josh Hawkes on the edge of the area who fired on goal beyond Oxley and Town were grateful to Eastman who cleared off the line.
Armstrong then dragged a shot wide in response, when he perhaps hesitated a touch believing he may have bee offside in the build-up.
Dacres-Cogley then went into the book for a shove on Levi Sutton before Oxley pulled off a fantastic save from a Mumbongo mis-hit shot that caught the Town keeper wrong-footed.
It was Mumbongo's last action as he was replaced by Kane Hemming's after 63 minutes before Simon Weaver made his first change soon after when Grant as replaced by Matt Daly.
Both Sutton and Turnbull went into the book for continuing their discussions too long for referee Gill's liking after a midfield clash.
Town should have had the lead from the resulting free-kick when Fouds's quick-thinking played in Olaigbe, whose shot was only parried by Hewelt but the onrushing Jack Muldoon couldn't apply the finish with the big Rovers keeper narrowing the angle.
Town made a double-change with fifteen minutes remaining when Sam Folarin and Alex Pattison replaced Sutton and Muldoon.
Saunders then fired an effort no more than a couple of feet over Oxley's bar as the home side began to mount the pressure in the final stages.
Olaigbe then struck straight at Hewelt not once, but twice, in the final minutes but the hosts held firm.
The point sees Town move onto 39 points, seven clear of Hartlepool with eight games to play ahead of the forthcoming Easter fixtures.
Tranmere: Hewelt, Dacres-Cogley, Davies, Turnbull, Bristow, Merrie, Hendry, Hughes (Burton, 81), Hawkes, Mumbongo (Hemmings, 63),Saunders.
Substitutes: Hoti, O'Connor, Chalmers, Taylor, Turner-Cooke.
Goal: Oxley (og, 35)
Booked: Dacres-Cogley (53), Turnbull (68)
TOWN: Oxley, Falkingham, Thomson, Grant (Daly, 67), Olaigbe, O'Connor, Sutton (Pattison,75), Muldoon (Folarin, 75), Armstrong, Foulds, Eastman.
Substitutes: Jamesom, Mattock, Burrell, McArdle.
Goal: Armstrong (3)
Booked: O'Connor (35), Falkingham (48), Sutton (68)
Referee: Sunny Gill.