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CSK needed 17 off the final over to qualify, but Dayal held his nerve despite being hit for a towering six by Dhoni off the first ball to seal it in the end for RCB.
After losing seven of their first eight matches, RCB embarked on a superb five-match winning spree, with Sunday's 47-run win over DC lifting them to fifth in the table with 12 points.
Mumbai Indians, who beat Sunrisers Hyderabad earlier on Sunday, entered the playoffs and will face Lucknow Super Giants in Wednesday's Eliminator game, while Gujarat Titans take on Chennai Super Kings in Tuesday's first Qualifier.
Punjab have made a change while RCB are unchanged from their previous match.
SRH were all out for 125 in 19.2 overs, with leggie Wanindu Hasaranga picking up 5/18.
Tewatia top scored with an unbeaten 43 as the Titans chased down RCB's total of 170/6.
Abhishek Sharma scored 47 as SRH chased down the modest target of 69 runs in just 8 overs.
Du Plessis was purchased by RCB for Rs 7 crore in the mega auction last month.
CSK became the first team to qualify for the knockout stage of IPL 2021 after beating SRH by six wickets.
Faf du Plessis (95 not out) and Deepak Chahar (4/29) were the standout performers for CSK.
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