It was a fine knock by Suresh Raina (52 off 35 balls), followed by skipper Mahendra Singh Dhoni's unbeaten 33 and opener Shane Watson's 39 runs which took the yellow brigade to a good total against the hosts.
Opting to bat first, the visitors were off to a quick start as openers Ambati Rayudu and Watson accumulated 19 runs from the first two overs.
However, the decent start was short-lived as Jofra Archer drew the first blood for the hosts, when a short-ball from him took an inside edge to shattered Rayudu's (12 off 9 balls) stumps in the third over.
The opener's fall saw Raina joining Watson in the middle and the duo helped Chennai recover from the early blow taking their side past the 50-run mark in 5.1 overs.
Both batmen further played sensibly and shared an 81-run partnership to help the yellow brigade cross 100-run mark in 11.1 overs.
With the Australian all-rounder inching towards his half-centrury, Archer struck again in the 12th over to pack back a good looking Watson on 39 runs and Chennai's scorecard reading 105/2.
On the other hand, Raina, who was then accompanied by skipper Dhoni, slammed his half century facing 32 balls however, the southpaw threw his wicket when he failed to read a googly by Ish Sodhi, giving an easy catch to Stuart Binny at short-fine leg.
With Chennai at 119/3 in 13 overs, Dhoni and Sam Billings (27 off 22) forged a 55-run partnership off 39 balls to put back things in control.
Billings departed in the final over while trying to take a single as wicket-keeper Jos Buttler's throw from behind demolised the Englishman's stump.
Dhoni remained unbeaten on 33 runs facing 23 balls, hitting a boundary and a six to help his side reach a fighting total of 176 runs.
For Rajasthan, Archer bagged couple of wickets but leaked 42 runs while Sodhi scalped one conceding 29 runs.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)