Alexander and Stars' captain Tristen Roberts had the Stars up 2-0 after one period. Strathroy knotted the game in the second period, scoring from a wild scramble in front of Stars' goalie Tyler Roberts, before capitalizing on a turnover.
"The second period was a little rocky for us. We knew going into the third we had to tighten it up," Alexander said.
Strathroy looked to build on their momentum with a early third period power play, but Mathieu Paris struck shorthanded for the Stars, with his team leading 18th goal of the season.
"Paris has been huge for us especially on the penalty kill," Alexander said. "He works hard and gets the job done."
The Rockets managed to even the score on that same power play, 80 seconds later. Defenceman Tristan Gerth restored the Stars' lead a minute later, Alexander potted his second goal of the night, on the power play, for a 5-3 lead. The Rockets made it interesting with seven minutes remaining.
St. Thomas held off a late Rockets' surge over the final two minutes, highlighted by Jackson Dobbin blocking a point shot with 25 seconds to go, just inside the Stars' blueline.
"That was absolutely huge," said Alexander. "He's been a grinder for us all year. Soaked shots like that night in and nigh out and can't win games without guys like that."
St. Thomas out shot Strathroy, 36-30.
The Stars, with a 13-21-3-1 record, have won back to back games, for the first time since winning three in a row, in late October. The club is 4-4-1-0, since the season resumed, Feb. 4.
"We're playing with a lot of competitiveness and intensity," said Paris, who leads the Stars with 36 points. "We've been jelling, we're closing out games and playing good as a squad."
Tristen Roberts has 14 goals and 15 assists, on the season and Alexander, 10 goals and 16 assists.
Eight games remain for the Stars, including at Strathroy, March 26. The Stars finish the regular season at home, hosting Saria, Sunday, April 3.
Four teams have clinched a playoff spot in the Western Conference: London, Leamington, Chatham and St. Marys.