The win snapped Knight Riders' six-match winning streak and perched Mumbai Indians to third position in the table with 16 points, one less than second-placed Kolkata.
Sharma entertained the packed Eden crowd with his 60-ball 109-run knock, studded with 17 boundaries including five sixes, while Gibbs made his Mumbai Indians debut in style with an unbeaten 66.
The duo shared an unconquered 167-run second-wicket partnership to propel Mumbai Indians to 182 for one after winning the toss.
Image: Mumbai Indians' Rohit Sharma raises his bat after scoring fifty runs during an Indian Premier League (IPL) cricket match against Kolkata Knight Riders in Kolkata, India, Saturday, May 12, 2012.
Scorecard | IPL 2012