diff --git a/jax/_src/pallas/triton/lowering.py b/jax/_src/pallas/triton/lowering.py
index b8e01bf55..d0dfd0eb7 100644
--- a/jax/_src/pallas/triton/lowering.py
+++ b/jax/_src/pallas/triton/lowering.py
@@ -18,7 +18,7 @@ from __future__ import annotations
 import dataclasses
 import functools
 import operator
-from typing import Any, Dict, Sequence, Tuple
+from typing import Any, Callable, Dict, Sequence, Tuple
 import zlib
 
 import jax
@@ -432,23 +432,39 @@ for primitive, fn in _TRITON_FN_MAPPING.items():
   triton_lowering_rules[primitive] = rule
 
 
-def _clamp_lowering_rule(ctx: TritonLoweringRuleContext, min, operand, max):
-  operand = tl.math.max(operand, min, _builder=ctx.builder)
-  return tl.math.min(operand, max, _builder=ctx.builder)
+def _integer_pow(a, *, y):
+  if y == 2:
+    return a * a
+  if y == 3:
+    return a * a * a
+  if y == -2:
+    return 1.0 / (a * a)
+  return jax.lax.pow(a, y)
 
 
-triton_lowering_rules[lax.clamp_p] = _clamp_lowering_rule
+def lower_fun(
+    fun: Callable[..., Any], *, multiple_results: bool
+) -> Callable[..., Any]:
+  fn = fun if multiple_results else lambda *args, **kw: (fun(*args, **kw),)
+
+  def f_lowered(ctx: TritonLoweringRuleContext, *args, **params):
+    wrapped_fun = lu.wrap_init(fn, params)
+    jaxpr, _, consts = pe.trace_to_jaxpr_dynamic(wrapped_fun, ctx.avals_in)
+    jaxpr = jax_core.ClosedJaxpr(jaxpr, consts)
+    out = _closed_call_lowering_rule(ctx, *args, call_jaxpr=jaxpr)
+    return out if multiple_results else out[0]
+
+  return f_lowered
 
 
-def _logistic_lowering_rule(ctx: TritonLoweringRuleContext, a):
-  one_ = tl.core._to_tensor(1.0, ctx.builder)
-  x = tl.exp(a.__neg__(_builder=ctx.builder), _builder=ctx.builder)
-  x = x.__add__(one_, _builder=ctx.builder)
-  x = one_.__truediv__(x, _builder=ctx.builder)
-  return x
+_JAX_FN_MAPPING = {
+    lax.clamp_p: lambda min, a, max: jnp.minimum(jnp.maximum(min, a), max),
+    lax.integer_pow_p: _integer_pow,
+    lax.logistic_p: lambda a: 1 / (1 + jnp.exp(-a)),
+}
 
-
-triton_lowering_rules[lax.logistic_p] = _logistic_lowering_rule
+for primitive, fn in _JAX_FN_MAPPING.items():
+  triton_lowering_rules[primitive] = lower_fun(fn, multiple_results=False)
 
 
 def _div_lowering_rule(ctx: TritonLoweringRuleContext, a, b):
@@ -471,21 +487,6 @@ def _iota_lowering_rule(
 triton_lowering_rules[lax.iota_p] = _iota_lowering_rule
 
 
-def _integer_pow_lowering_rule(ctx: TritonLoweringRuleContext, a, *, y):
-  if y == 2:
-    return a.__mul__(a, _builder=ctx.builder)
-  if y == 3:
-    return a.__mul__(a.__mul__(a, _builder=ctx.builder), _builder=ctx.builder)
-  if y == -2:
-    one_ = tl.core._to_tensor(1.0, ctx.builder)
-    a_sq = a.__mul__(a, _builder=ctx.builder)
-    return one_.__truediv__(a_sq, _builder=ctx.builder)
-  return tl.math.pow(a, y, _builder=ctx.builder)
-
-
-triton_lowering_rules[lax.integer_pow_p] = _integer_pow_lowering_rule
-
-
 def _convert_element_type_lowering_rule(
     ctx: TritonLoweringRuleContext, a, *, new_dtype, weak_type
 ):