Alonso, who was making his 100th Champions League appearance, was dismissed with 25 minutes remaining following a second booking from Spanish referee Alberto Undiano Mallenco.
Bayern, who trounced Hamburg 8-0 in the Bundesliga on Saturday, were stifled by a Shakhtar side, playing their first competitive game in two months.
Shakhtar's solid rearguard display maintained their chances of reaching the Champions league quarter-finals for the second time while Guardiola’s Bayern will need to adopt a less cautious approach in the return leg in Munich on March 11.
“I am especially pleased with the opening spell of the game when our players created three or four options to open the scoring and controlled the ball,” Bayern coach Pep Guardiola told reporters.
“Our task was to restrain Shakhtar’s quick players from unfolding counter attacks. I am happy that we coped with this as they had zero goal chances."
Shakhtar boss Mircea Lucescu, however, was left ruing a missed opportunity.
"I only regret we did not start to play our usual football after Xabi Alonso was sent off," he said.
SCRAPPY GAME
Bayern came into the clash full of confidence and were quickly on the front foot with Arjen Robben, Franck Ribery and Thomas Mueller creating good chances.
Robben out-muscled Shakhtar defender Vyacheslav Shevchuk in the penalty area and fed Thomas Muller, whose shot rolled along the goalline, before being cleared to the relief of the home supporters.
It was a scrappy game undermined by a number of niggly fouls with tempers flaring on several occasions.
Mueller spurned a glorious chance after 30 minutes when he fired a volley over the bar after being superbly set up by Ribery.
Emotions boiled over in the second half with Brazilian midfielder Douglas Costa booked for lashing out at Ribery before Alonso, who had already been yellow carded in the first half, was sent off on 65 minutes for upending Alex Teixeira.
This forced Bayern onto the back foot and left them trying to hit Shakhtar on the break with quick counters.
Bayern boss Guardiola tried to inject some attacking impetus by bringing on Robert Lewandowski, but both sides appeared happy to settle for a draw as the game drew to a close.
(Editing by Toby Davis)
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