Kohli, the standard bearer for Indian cricket, has now scored just 119 runs from eight matches.
Three balls later, the same Jansen-Markram combination accounted for opener Anuj Rawat to leave Bangalore reeling at 8-3. Jansen finished with 3-25 from his four overs.
Bangalore were unable to recover and kept losing wickets to go down to the lowest total of this season in 16.1 overs. It was the sixth lowest total ever in the IPL.
Only Glenn Maxwell (12) and Suyash Prabhudessai (15) got into double figures.
Hyderabad romped home with 12 overs to spare and move second in the 10-team table led by Gujarat Titans who beat Kolkata Knight Riders by eight runs in the first match of the day.
Bangalore, still searching for their maiden title in the Twenty20 tournament, hold the dubious record of the lowest ever score of 49 against Kolkata Knight Riders in 2017.
The dismal batting show got to the in-form Dinesh Karthik who fell caught behind for nought after Hyderabad successfully reviewed the umpire's initial not out decision.
T Natarajan took three wickets and left-arm spinner Jagadeesha Suchith took two.
Speedster Umran Malik kept the speed gun busy and got the pace up to 151 kmph (93.8 mph) as he took one wicket for 13 runs from his four overs.
The batters had their task cut out as openers Abhishek Sharma, who hit 47 off 28 deliveries, and skipper Kane Williamson, who made an unbeaten 16, put on 64 runs.
Harshal Patel denied Abhishek his fifty as the batsman was caught out at long on and Rahul Tripathi came out to hit the winning six to hand Hyderabad their fifth straight win.