Anthony Stokes curled home a late free-kick against Dundee United to round off a rewarding week for Celtic.
The visitors began the brighter, with Stokes volleying wide and Virgil van Dijk firing over.
United eventually responded with David Goodwillie's downward header and Nadir Ciftci's lofted free-kick testing goalkeeper Fraser Forster.
The players produced little to excite in the second half until Stokes despatched his free-kick with aplomb.
Having reached the Champions League group stage thanks to their 3-0 win over Shakhter Karagandy on Wednesday, Celtic manager Neil Lennon had intimated that he wants his players to deliver improved results in the matches that follow European exertions.
His message seemed to have registered, because there was a verve to the visitors' play from the first whistle.
Unusually, four of Celtic's five chances in the opening half hour came from their defensive players.
In the second minute, full-back Mikael Lustig drifted into the United box and, although he got a powerful shot away, it was blocked by Sean Dillon.
Then van Dijk picked up the ball on the halfway line, saw the gap in the tangerine ranks and surged into the danger zone almost uncontested. His left-footed finish over the bar betrayed his normal central-defensive role.
With United struggling to keep pace, Honduran left-back Emilio Izaguirre showed he too had the appetite for domestic fare as he made himself available on the overlap and his cross was punched clear by home goalkeeper Radoslaw Cierzniak.
The Terrors inched their way into the match, tackling with vigour in midfield, but still the green and white shirts advanced.
When Stokes' 17th-minute volley whizzed past the left-hand post and, within a minute, van Dijk's thunderous 22-yard shot darted past the other post, Cierzniak could have been forgiven for feeling disorientated.
However, in the final 15 minutes of the first half, it was United who had the upper hand.
Defender Andy Robertson shot over Forster's crossbar from a tight angle then the English goalie kept out a Goodwillie header from Paul Paton's perfect cross from the left.
The Taysiders' best chance, though, came from Ciftci's 20-yard free-kick. The Dutch-born Turk clipped the ball firmly over the Celtic wall but was denied a goal by the strong outstretched hand of Forster as the goalkeeper dived to his right.
Commons was the player who further brightened the match at sun-drenched Tannadice.
Within five minutes of the restart, he had created two chances down the right, the first of which he fired low at goal after cutting on to his favoured left foot, then he slipped the ball between a United trio and squeezed into the box before his cutback was cleared.
Lustig was stretchered off with a painful ankle after landing awkwardly from an aerial challenge with Gavin Gunning, with striker Amido Balde his replacement.
This typified the scrappiness of the match at that stage as a series of fouls, over-hit passes and offside decisions prevented any sense of momentum in the play.
Gary Mackay-Steven clipped Stokes to present the Irishman with a free-kick in an attractive position just outside the box, but the visiting striker's effort lacked craft and cannoned off the United wall.
Home manager Jackie McNamara replaced Goodwillie with 17-year-old Ryan Gauld, but it was another of his young players, Robertson, who caught the eye with a testing cross from the left that caught Forster flat-footed.
Ten minutes from time, Mackay-Steven's dance towards the Celtic goal was halted by van Dijk's illegal block in the D.
Gauld's free-kick did not progress beyond the wall and the match seemed destined for the first goalless meeting between the teams in 19 years.
However, Stokes made United pay for Stuart Armstrong's foul on him as he ran into the penalty area. He curled the subsequent free-kick in off the left-hand post to give Celtic the win.