Australia needed to bat out the final day to avoid defeat, and faced an uphill task when resuming on 59-4 this morning, before slipping to 117-7 by lunch.
Johnson continued his resilient knock, adding nine more runs to his total from tea to top the scoring with 61, and his dismissal sent Steve O'Keefe to the crease with Peter Siddle to attempt to see out the remaining overs.
However, the debutant spinner was unable to get off the mark as Zulfiqar Babar managed to claim the wicket of Siddle for 15 to end the innings and the match.
Babar finished the innings with 5-74, having also picked up two wickets in the first innings, while Yasir Shah claimed 4-50.
The second Test begins in Abu Dhabi on Thursday.