The paper "Aspirin compared with acetaminophen in the treatment of fever and other symptoms of upper respiratory tract infection in adults", published by the NIH, tested the efficacy of Aspirin, Acetaminophen (Paracetamol), and a Placebo for fever reduction.
(In the USA, Paracetamol is commonly known as Acetaminophen.)
They tested 392 patients at two different dosing levels for aspirin and acetaminophen (78 in both aspirin groups, 79 in both acetaminophen groups, 78 in the placebo group).
Resulting mean maximum temperature reductions and the Area Under the Curve (AUC) for four hours after dosing were:
500 mg Aspirin: 1.32 °C, 3.18 AUC
1000 mg Aspirin: 1.25 °C, 4.26 AUC
500 mg Acetaminophen: 1.67 °C, 3.13 AUC
1000 mg Acetaminophen: 1.71 °C, 4.11 AUC
Placebo: 0.63 °C, 0.76 AUC
Note that this study included only adults, the efficacy of paracetamol by itself in children with fevers has been questioned
This "Ask the Professor" article in the Tufts Journal suggests the mechanism by which Acetaminophen and similar drugs reduce fever:
By blocking COX and, therefore, the subsequent production of
prostaglandins in the central and peripheral nervous systems,
non-opioid analgesics reduce both fever and inflammation.