diff --git a/promql/functions.go b/promql/functions.go
index 9af904c9e6..2577e7f27b 100644
--- a/promql/functions.go
+++ b/promql/functions.go
@@ -144,32 +144,37 @@ func extrapolatedRate(vals []parser.Value, args parser.Expressions, enh *EvalNod
 	// (which is our guess for where the series actually starts or ends).
 
 	extrapolationThreshold := averageDurationBetweenSamples * 1.1
-	extrapolateToInterval := sampledInterval
-
 	if durationToStart >= extrapolationThreshold {
 		durationToStart = averageDurationBetweenSamples / 2
 	}
-	if isCounter && resultFloat > 0 && len(samples.Floats) > 0 && samples.Floats[0].F >= 0 {
+	if isCounter {
 		// Counters cannot be negative. If we have any slope at all
 		// (i.e. resultFloat went up), we can extrapolate the zero point
 		// of the counter. If the duration to the zero point is shorter
 		// than the durationToStart, we take the zero point as the start
 		// of the series, thereby avoiding extrapolation to negative
 		// counter values.
-		// TODO(beorn7): Do this for histograms, too.
-		durationToZero := sampledInterval * (samples.Floats[0].F / resultFloat)
+		durationToZero := durationToStart
+		if resultFloat > 0 &&
+			len(samples.Floats) > 0 &&
+			samples.Floats[0].F >= 0 {
+			durationToZero = sampledInterval * (samples.Floats[0].F / resultFloat)
+		} else if resultHistogram != nil &&
+			resultHistogram.Count > 0 &&
+			len(samples.Histograms) > 0 &&
+			samples.Histograms[0].H.Count >= 0 {
+			durationToZero = sampledInterval * (samples.Histograms[0].H.Count / resultHistogram.Count)
+		}
 		if durationToZero < durationToStart {
 			durationToStart = durationToZero
 		}
 	}
-	extrapolateToInterval += durationToStart
 
 	if durationToEnd >= extrapolationThreshold {
 		durationToEnd = averageDurationBetweenSamples / 2
 	}
-	extrapolateToInterval += durationToEnd
 
-	factor := extrapolateToInterval / sampledInterval
+	factor := (sampledInterval + durationToStart + durationToEnd) / sampledInterval
 	if isRate {
 		factor /= ms.Range.Seconds()
 	}
diff --git a/promql/promqltest/testdata/native_histograms.test b/promql/promqltest/testdata/native_histograms.test
index c4ffcba034..b223e90c30 100644
--- a/promql/promqltest/testdata/native_histograms.test
+++ b/promql/promqltest/testdata/native_histograms.test
@@ -1041,11 +1041,15 @@ eval_warn instant at 1m rate(some_metric[1m30s])
 eval_warn instant at 1m30s rate(some_metric[1m30s])
     # Should produce no results.
 
-# Start with custom, end with exponential. Return the exponential histogram divided by 30.
+# Start with custom, end with exponential. Return the exponential histogram divided by 48.
+# (The 1st sample is the NHCB with count:1. It is mostly ignored with the exception of the
+# count, which means the rate calculation extrapolates until the count hits 0.)
 eval instant at 1m rate(some_metric[1m])
-    {} {{schema:0 sum:0.16666666666666666 count:0.13333333333333333 buckets:[0.03333333333333333 0.06666666666666667 0.03333333333333333]}}
+    {} {{count:0.08333333333333333 sum:0.10416666666666666 counter_reset_hint:gauge buckets:[0.020833333333333332 0.041666666666666664 0.020833333333333332]}}
 
 # Start with exponential, end with custom. Return the custom buckets histogram divided by 30.
+# (With the 2nd sample having a count of 1, the extrapolation to zero lands exactly at the
+# left boundary of the range, so no extrapolation limitation needed.)
 eval instant at 30s rate(some_metric[1m])
     {} {{schema:-53 sum:0.03333333333333333 count:0.03333333333333333 custom_values:[5 10] buckets:[0.03333333333333333]}}
 
@@ -1376,21 +1380,25 @@ eval instant at 1m histogram_fraction(-Inf, +Inf, histogram_nan)
 
 clear
 
-# Tests to demonstrate how an extrapolation below zero is prevented for a float counter, but not for native histograms.
-# I.e. the float counter that behaves the same as the histogram count might yield a different result after `increase`.
+# Tests to demonstrate how an extrapolation below zero is prevented for both float counters and native counter histograms.
+# Note that the float counter behaves the same as the histogram count after `increase`.
 
 load 1m
   metric{type="histogram"} {{schema:0 count:15 sum:25 buckets:[5 10]}} {{schema:0 count:2490 sum:75 buckets:[15 2475]}}x55
   metric{type="counter"} 15 2490x55
 
 # End of range coincides with sample. Zero point of count is reached within the range.
+# Note that the 2nd bucket has an exaggerated increase of 2479.939393939394 (although
+# it has a value of only 2475 at the end of the range).
 eval instant at 55m increase(metric[90m])
-    {type="histogram"} {{count:2497.5 sum:50.45454545454545 counter_reset_hint:gauge buckets:[10.09090909090909 2487.409090909091]}}
+    {type="histogram"} {{count:2490 sum:50.303030303030305 counter_reset_hint:gauge buckets:[10.06060606060606 2479.939393939394]}}
     {type="counter"} 2490
 
 # End of range does not coincide with sample. Zero point of count is reached within the range.
+# The 2nd bucket again has an exaggerated increase, but it is less obvious because of the
+# right-side extrapolation.
 eval instant at 54m30s increase(metric[90m])
-    {type="histogram"} {{count:2520.8333333333335 sum:50.92592592592593 counter_reset_hint:gauge buckets:[10.185185185185187 2510.6481481481483]}}
+    {type="histogram"} {{count:2512.9166666666665 sum:50.76599326599326 counter_reset_hint:gauge buckets:[10.153198653198652 2502.7634680134674]}}
     {type="counter"} 2512.9166666666665
     
 # End of range coincides with sample. Zero point of count is reached outside of (i.e. before) the range.