In their first appearance in the 46th edition of the traditional Swiss Uhrencup in Grenchen, Celtic got the better of the 10-time winners at the Bruhl Stadium in front of a sell-out 8,612 crowd, with Miller finding the target three minutes before half-time.

Strachan’s side was captained by Steven Pressley, a contender to take over that role from Neil Lennon on a permanent basis, and made a promising start when Maciej Zurawski’s volley hit the crossbar in the second minute after a perfect cross from Mark Wilson.

Only three minutes later Aiden McGeady, who is targeting a double-figure goal return in the coming season, saw his confident shot from 20 yards go just narrowly wide.

Basle manager Christian Gross, the former Tottenham boss, fielded a starting XI which featured just three regular first-team players.

Brazilian striker Eduardo had Basle’s first chance when he eased past Pressley and hit a fierce shot which Mark Brown did well to keep out.

In the 12th minute Basle’s Cabral seized on Thomas Gravesen’s short back-pass to give Celtic another scare which again they survived, and within seconds Zurawski was threatening at the other end.

He had his second attempt at goal after a cross from McGeady, and the Polish striker’s close-range header was miraculously kept out by Basle goalkeeper Franco Costanzo.

In an open match, the chances flowed and Basle’s Ivan Ergic shot just inches wide before Eduardo spurned a series of chances.

Miller fired a warning in the 37th minute when, following a counter-attack, his powerful volley sailed narrowly wide.

And he made the breakthrough five minutes later after a shocking mistake by Basle central defender Francois Marque.

Midfield prospect Teddy Bjarnason reacted to the defender’s slip-up and his short pass found Miller who calmly fired past Costanzo to give Celtic a half-time advantage.

At half-time, Strachan overlooked the tournament rules which allow for a maximum of six substitutions and brought on nine players, with only Wilson and Pressley staying on the pitch.

Basle made the better start to the second half with a series of corner kicks and a powerful shot from Franz Burgmeier from almost 30 yards which substitute goalkeeper Michael McGovern struggled to save.

Wilson came close to a second goal following a corner, when his 20-yard strike just missed the target, and Jiri Jarosik’s deflected shot went inches wide, to the relief of Costanzo.

Improving Celtic then caused more trouble for Costanzo when former Motherwell striker Scott McDonald, on his debut, was left unmarked and had a close-range chance but failed to convert his header.

McDonald’s fellow Australian could have snatched an equaliser in the 79th minute when Fabian Frei played him a smart pass, but from a position alone in front of goal he failed to beat McGovern.

Celtic’s summer signing from AC Milan Massimo Donati had an understated debut in central midfield, seeing little of the ball, and was among the players replaced at half-time by Strachan, with £4.4m former Hibernian man Scott Brown getting his first run-out after the break.