For the third time this season, the Blues entered a game with a chance to get a season-high four games above .500. For the third time this season, they fell short, losing 5-3 Saturday to the Chicago Blackhawks at Enterprise Center.

Granted, four games above .500 doesn’t sound like much. But it has been an impossible hurdle to clear for the Blues this season.

The Blues started the season 3-0-0, and then lost a franchise record eight straight.

On the first game of this homestand, they moved to 21-18-3 after rallying for a 4-3 overtime win against Calgary. Only to lose their next two games.

And now, after Saturday’s setback, they are 23-21-3 and just 3-3 on this season-long seven-game homestand. Obviously, there’s much work to do to earn a playoff berth. And they’ve pretty much squandered a chance to stack points on this homestand.

Despite its lowly overall record of 14-26-4, Chicago is on a roll — having won six of its last seven games. Until Saturday, the Blues had owned the Blackhawks lately. They were 9-0-2 against their Central Division rivals over their prior 11 matchups, the longest point streak against Chicago in franchise history.

But no more.

Down 4-2 after two periods, Nick Leddy’s first goal of the season cut the Chicago lead to 4-3 at the 9:15 mark of the third period and the Blues pressured the Blackhawks for the tying goal.

But with 3:59 left in the game, Max Domi scored to restore the Blackhawks’ two-goal lead.

The Blues outshot the Blackhawks 11-3 in a bizarre opening period, had two power plays, but somehow found themselves trailing 2-0 after the opening period. Overall shot attempts were 22-5 for St. Louis.

But the Blackhawks scored on their first two shots on goal to take the lead. That’s right — two shots on goal, two goals for Chicago.

The first goal came on an impromptu 2-on-1 that developed when Colton Parayko collided with a Chicago player at center ice and was taken out of the play, and then Josh Leivo got beat near the blue line by Sam Lafferty.

That created the 2-on-1 and Jason Dickinson scored from Lafferty backdoor to make it a 1-0 game at the 10:27 mark of the first. That was shot No. 1 for Chicago.

Shot No. 2 came while the Blues were on their second power play, with Jake McCabe off for tripping Bandon Saad. With an ineffective St. Louis power play winding down, Saad lost the puck along the boards in the Blues’ offensive zone to Dickinson.

Dickinson in turn, sent the puck ahead to Lafferty, who had a breakaway and beat Binnington five-hole with 6:40 remaining in the opening period.

Binnington has played some strong hockey in recent starts, but after yielding four goals on just seven Chicago shots, he was done for the evening.

After Andrea Athanasiou scored his third goal in three games this season against Binnington, the Blues’ goalie was pulled in favor of Thomas Greiss just 3:59 into the second period. It marked the third time Binnington has been pulled in 36 starts this season, but the first time since Dec. 3 in Pittsburgh.

It’s not like any of the four goals would’ve been easy saves, but in order to play winning hockey, you hope your goalie stops one of two of them.

The Blues got a power play goal by Jordan Kyrou, his 22nd of the season, and a net-front back-hand goal by Ivan Barbashev in the second period. Barbashev’s even-strength goal was his seventh of the season and first since Jan. 5 in New Jersey.

But the Blackhawks countered with goals by Reese Johnson and Athanasiou to take a 4-2 lead into the third period. Johnson’s goal came when he outmuscled Calle Rosen at the net front to give Chicago a 3-0 lead just two minutes into the second.

Just 1 ½ minutes after Barbashev’s goal, which made it 4-2 with 6:48 left in the period, he got into a fight with Chicago’s Isaak Phillips. Phillips may have taken offense to a hit by Barbashev on Dickinson, which took place just seconds before the fight.

It was Barbashev’s second fight of the season and the Blues’ third fight in as many games.

There were a couple of other shoving matches before the period ended, one of which left the Blues on the penalty kill for two minutes to start the third period. After the buzzer sounded to end the second period, Pavel Buchnevich flipped the puck down towards the Chicago goal.

Blackhawks goalie Jaxson Stauber was well out of the crease, heading off the ice, when the puck reached him. Chicago took offense and shoved Buchnevich. Buchnevich shoved back.

Much to the chagrin of the Blues, Buchnevich got two minutes for roughing and two more minutes for unsportsmanlike conduct. Chicago’s Lafferty got two minutes for roughing. That meant the Blues began the third period with two minutes of a penalty to kill off.