It turns out they both did on the same night.
Gomez and Burish notched their first goals of the season and Joe Pavelski scored the shootout winner as the San Jose Sharks held on to defeat the Vancouver Canucks 3-2 on Tuesday.
"The win is the most important thing, but it does feel nice to score," said Gomez, who has a goal and two assists in 15 games this season. "Obviously it was time. I know I can score. It's just you've got to shoot to score, and sometimes I have trouble with that. I'm always looking to pass."
Burish, meanwhile, scored his first goal in 45 games on a short-handed breakaway to make it 2-0 San Jose early in the second period.
"If I start going out there thinking that I've got to score I'm doing my linemates and my teammates a disservice," said Burish. "I've got to focus on other things: I've got to be solid defensively, I've got to kill penalties, I've got to bring energy. But if you can score goals, it feels a little better, too."
Brad Stuart added two assists and Antti Niemi made 36 saves for the Sharks (11-6-4), who won their second straight game after a stretch that saw them go 2-6-4.
Henrik Sedin and Jannik Hansen replied for Vancouver (11-6-5), which dropped to 3-4-3 in its past 10 games after starting the season 8-2-2.
"Our record isn't as good of late but we know we can play some better hockey," said Canucks forward Mason Raymond.
The Sharks started the season on fire, reeling off seven straight victories, but their offence suddenly dried up. Heading into the game versus Vancouver, they sat tied with Nashville for the fewest goals in the NHL (47).
Although the Sharks didn't exactly overwhelm Vancouver with offence, they came on strong in the third period and fired seven shots at Cory Schneider in overtime.
In the shootout, Logan Couture had to score in the third round or the Sharks would lose.
Couture calmly deked to the backhand and beat Schneider between the legs.
After Niemi stopped Alex Burrows in the fourth round, Pavelski broke in and beat Schneider with a quick wrist shot to the blocker side to end it.
"You're always excited to win," said Pavelski. "It's not looking good there for a second, and then within a minute or two you've got a chance to win it. ... It's going to take more than two probably most nights, but if we can get two or three it's going to give us a good chance to win."
Chris Higgins had Vancouver's lone shootout tally, beating Niemi on the blocker side.
The teams were tied 2-2 after two periods.
The Canucks fell behind 2-0 early in the second frame, but it was their top line that gave them life.
Daniel Sedin flipped the puck in front of the net and it took a fortuitous bounce to Henrik Sedin, who went to the backhand to beat Niemi at 13:23.
With 25 seconds remaining in the middle period, Hansen fired a quick wrist shot that Niemi never saw for his sixth goal of the season. For Hansen, normally a grinder, it was his fifth point in the past three games.
The Sharks opened up their lead thanks to Gomez and Burish.
Gomez took a soft slap shot from about 45 feet out that hit the crossbar and went in. Schneider appeared to be screened.
Despite a resume that includes two Stanley Cups, Gomez has struggled in recent years and was bought out of his contract by the Montreal Canadiens in the off-season. It had an annual cap hit of $7.3 million. He was happy to sign a one-year deal with the Sharks for $700,000.
"I'm just enjoying each day now," said Gomez, who has 10 goals in his past 133 NHL games.
Niemi has been San Jose's bright light this season, and he continued his strong play.
With Vancouver pressing for the winner late in the third period, he robbed Burrows and Henrik Sedin with nifty pad saves.
He had luck on his side, too, as Jason Garrison hit the post with a minute remaining.
In overtime, the Sharks killed off a two-minute Canucks power play with Gomez in the box for goaltender interference.
"What can you say about Nemo, he was definitely the story again tonight," said Gomez.
Vancouver, meanwhile, had plenty of chances to win, but couldn't convert on any of their five dangerous-looking power plays.
It's the sixth straight game the Canucks have failed to score with the man advantage.
"In the third period they did everything they could but beat the goaltender," Canucks coach Alain Vigneault said of the power play. “The looks were there, the opportunities were there, their goalie made the saves."
NOTES: Sharks coach Todd McLellan earned his 206th victory with the Sharks, tying Ron Wilson for the franchise record. ... Stuart lost teeth killing a penalty in the third period, and blocked four shots. "Stuey, luckily you guys don't get to see him naked but he's black and blue with bruises," said Burish. "It looks like he went through a meat grinder." ... Canucks D Keith Ballard drew back into the line-up after being a healthy scratch the past two games. He left the game midway through the third period with a charley horse and will be re-evaluated on Wednesday. ... D Cam Barker also dressed for his second straight game, while Kevin Bieksa (groin) and Andrew Alberts (healthy scratch) did not dress. ... Martin Havlat (lower body), T.J. Galiardi (healthy scratch) and Justin Braun (healthy scratch) did not dress for San Jose.