Boulter navigated a tricky match filled with twists and turns against Tomljanovic in her first singles match of the season on grass.
The 28-year-old came through a tense deciding set to book a last-16 meeting with fifth seed Diana Shnaider.
But, having slipped in the rankings this year while Raducanu has quietly crept back up, Boulter could end the tournament having lost her status as Britain's leading woman, which she has held since June 2023.
The two have paired up for the doubles event at Queen's and Boulter said she is happy to see Raducanu pushing her for top spot in the singles.
"Obviously, it holds a massive privilege being that person, but as I have said for the last two years which I have held that position, I'm not focused on necessarily that. I'm focused on myself and keeping my ranking up where I want it to be," Boulter said.
The pair are on opposite sides of the draw at Queen's, meaning they could not meet until the final.
But Raducanu will need to equal or better Boulter's run to regain her status as British number one, a position she held following her 2021 US Open win until Boulter took over.
The 22-year-old was keen to play down the significance of the rankings.
"The tournament is still young and Katie can go on a rip this week as well. Honestly, it's nice in a way having something to chase at one, but we have such a great relationship that it's a very healthy competition," she said.
Raducanu and Boulter will set the friendly domestic rivalry aside on Wednesday when they team up to take on top seeds Lyudmyla Kichenok and Erin Routliffe in the doubles after the top-seeded pair from Ukraine and New Zealand beat Britain's Kartal and Jodie Burrage 7-6 (10-8) 7-6 (7-1).