diff --git a/pkg/tsdb/influxdb/flux/flux.go b/pkg/tsdb/influxdb/flux/flux.go
index 18d2a6f725a..cab5c0d1067 100644
--- a/pkg/tsdb/influxdb/flux/flux.go
+++ b/pkg/tsdb/influxdb/flux/flux.go
@@ -31,7 +31,10 @@ func Query(ctx context.Context, dsInfo *models.DatasourceInfo, tsdbQuery backend
 	for _, query := range tsdbQuery.Queries {
 		qm, err := getQueryModel(query, timeRange, dsInfo)
 		if err != nil {
-			tRes.Responses[query.RefID] = backend.DataResponse{Error: err}
+			tRes.Responses[query.RefID] = backend.DataResponse{
+				Error:       err,
+				ErrorSource: backend.ErrorSourceDownstream,
+			}
 			continue
 		}
 
diff --git a/pkg/tsdb/influxdb/influxql/influxql.go b/pkg/tsdb/influxdb/influxql/influxql.go
index e7de3267e6f..651df59e3c7 100644
--- a/pkg/tsdb/influxdb/influxql/influxql.go
+++ b/pkg/tsdb/influxdb/influxql/influxql.go
@@ -30,6 +30,7 @@ const (
 
 var (
 	ErrInvalidHttpMode = errors.New("'httpMode' should be either 'GET' or 'POST'")
+	ErrInvalidUrl      = errors.New("URL must contain scheme and host")
 	glog               = log.New("tsdb.influx_influxql")
 )
 
@@ -51,13 +52,17 @@ func Query(ctx context.Context, tracer trace.Tracer, dsInfo *models.DatasourceIn
 			reqQuery := req.Queries[idx]
 			query, err := models.QueryParse(reqQuery, logger)
 			if err != nil {
-				return err
+				responseLock.Lock()
+				response.Responses[query.RefID] = backend.DataResponse{
+					Error:       err,
+					ErrorSource: backend.ErrorSourceDownstream,
+				}
+				responseLock.Unlock()
+				return nil
 			}
 
-			rawQuery, err := query.Build(req)
-			if err != nil {
-				return err
-			}
+			// query.Build() unconditionally returns nil for error.
+			rawQuery, _ := query.Build(req)
 
 			query.RefID = reqQuery.RefID
 			query.RawQuery = rawQuery
@@ -68,7 +73,13 @@ func Query(ctx context.Context, tracer trace.Tracer, dsInfo *models.DatasourceIn
 
 			request, err := createRequest(ctx, logger, dsInfo, rawQuery, query.Policy)
 			if err != nil {
-				return err
+				responseLock.Lock()
+				response.Responses[query.RefID] = backend.DataResponse{
+					Error:       err,
+					ErrorSource: backend.ErrorSourceDownstream,
+				}
+				responseLock.Unlock()
+				return nil
 			}
 
 			resp, err := execute(ctx, tracer, dsInfo, logger, query, request, features.IsEnabled(ctx, featuremgmt.FlagInfluxqlStreamingParser))
@@ -90,13 +101,15 @@ func Query(ctx context.Context, tracer trace.Tracer, dsInfo *models.DatasourceIn
 		for _, reqQuery := range req.Queries {
 			query, err := models.QueryParse(reqQuery, logger)
 			if err != nil {
-				return &backend.QueryDataResponse{}, err
+				response.Responses[query.RefID] = backend.DataResponse{
+					Error:       err,
+					ErrorSource: backend.ErrorSourceDownstream,
+				}
+				continue
 			}
 
-			rawQuery, err := query.Build(req)
-			if err != nil {
-				return &backend.QueryDataResponse{}, err
-			}
+			// query.Build() unconditionally returns nil for error.
+			rawQuery, _ := query.Build(req)
 
 			query.RefID = reqQuery.RefID
 			query.RawQuery = rawQuery
@@ -107,7 +120,11 @@ func Query(ctx context.Context, tracer trace.Tracer, dsInfo *models.DatasourceIn
 
 			request, err := createRequest(ctx, logger, dsInfo, rawQuery, query.Policy)
 			if err != nil {
-				return &backend.QueryDataResponse{}, err
+				response.Responses[query.RefID] = backend.DataResponse{
+					Error:       err,
+					ErrorSource: backend.ErrorSourceDownstream,
+				}
+				continue
 			}
 
 			resp, err := execute(ctx, tracer, dsInfo, logger, query, request, features.IsEnabled(ctx, featuremgmt.FlagInfluxqlStreamingParser))
@@ -129,6 +146,13 @@ func createRequest(ctx context.Context, logger log.Logger, dsInfo *models.Dataso
 		return nil, err
 	}
 
+	// It's possible that the configuration is bad, and we'll have a URL
+	// without a scheme or host. This is valid from the PoV of the Go std
+	// library url.Parse(), but not for this data source.
+	if u.Host == "" || u.Scheme == "" {
+		return nil, ErrInvalidUrl
+	}
+
 	u.Path = path.Join(u.Path, "query")
 	httpMode := dsInfo.HTTPMode
 
diff --git a/pkg/tsdb/influxdb/models/model_parser.go b/pkg/tsdb/influxdb/models/model_parser.go
index 011066b4ef9..90f8985fc75 100644
--- a/pkg/tsdb/influxdb/models/model_parser.go
+++ b/pkg/tsdb/influxdb/models/model_parser.go
@@ -1,6 +1,7 @@
 package models
 
 import (
+	"errors"
 	"fmt"
 	"strconv"
 	"time"
@@ -12,6 +13,10 @@ import (
 	"github.com/grafana/grafana/pkg/infra/log"
 )
 
+var (
+	ErrInvalidQuery = errors.New("invalid InfluxDB query")
+)
+
 type InfluxdbQueryParser struct{}
 
 func QueryParse(query backend.DataQuery, logger log.Logger) (*Query, error) {
@@ -33,17 +38,17 @@ func QueryParse(query backend.DataQuery, logger log.Logger) (*Query, error) {
 
 	tags, err := parseTags(model)
 	if err != nil {
-		return nil, err
+		return nil, errors.Join(ErrInvalidQuery, err)
 	}
 
 	groupBys, err := parseGroupBy(model)
 	if err != nil {
-		return nil, err
+		return nil, errors.Join(ErrInvalidQuery, err)
 	}
 
 	selects, err := parseSelects(model)
 	if err != nil {
-		return nil, err
+		return nil, errors.Join(ErrInvalidQuery, err)
 	}
 
 	interval := query.Interval