Cockburn defender Kieron Stallard was sent off after only 24 minutes, but second-half goals to Dean Evans and Gareth McGlynn saw the Lions take home the three points.
It was a tight opening with the best chances falling to the visitors on the quarter hour with Miki Vujacic’s cross headed just over the top by Phil Arnold.
The 10 men steadied and Jack Eades’ shot from the edge of the box flashed wide, and moments later Harry O’Brien fired straight at Aleks Vrteski when well placed.
The Lions were struggling to break down the home defence ” the best chance fell to Vujacic on 40 minutes, whose long-range shot went over the crossbar.
Stirling made a change at the break, bringing on Moses Kalau who caused problems down the flanks.
Cockburn were hitting on the counter attack and in the 77th minute O’Brien made a run down the right and his low cross was only inches away from Antonio Naglieri at the back post.
With time running out for Stirling, their patience was rewarded with the lead on 84 minutes.
Kalau wriggled his way past three Cockburn defenders on the left, played a one-two with Arnold, and his cross picked out Evans who fired home from five-meters.
Two minutes into stoppage time Stirling added a second. Matthew Harold’s cross from the left was dummied by Sam Fuzik in the penalty area and McGlynn fired home from 10m.
The Lions Under 18s came out on top with a 3-2 win while the Reserves were defeated 2-1.
Stirling will return to Macedonia Park on Saturday to meet ECU Joondalup, kick-off at 3pm.
In other games, Bays-water City defeated Perth 8-0 and Balcatta drew 2-all against Armadale.