It’s odd to watch a match and conclude that experience pulled the winner through, when that player is just 20 years old. But that was the case tonight, as Sloane Stephens put down the Australian Open insurgency of 19-year-old Elina Svitolina in a third-round match, prevailing 7-5, 6-4.

It seems like these two ladies are destined to have many more meetings, some of them surely in later stages than the one in which they just made each other’s acquaintance. Stephens did well to get through this one in straight sets, and her ability to close out a match that nearly got away from her is an encouraging sign going forward.

Stephens was up 3-1 in the opening set, fell behind 3-5, but regained control—and then avoided playing the kind of loose service game(s) that has undercut her efforts in the past. This is a player who has needed to tighten up her game; today she cranked the screws so hard that you could almost hear the wood splinter.

Svitolina popped on the radar in Melbourne with her first-round upset of No. 19 seed and two-time Grand Slam champion Svetlana Kuznetsova. But she was already one of just two teenagers ranked inside the Top 50 (the other one is Madison Keys), and she wasted no time demonstrating why she’s held in high regard by many pundits.

Svitolina is an extremely well-balanced, versatile player. Her backhand is rock solid; her forehand is dangerous if, true to script, just slightly less reliable. She moves well for a young lady with a substantial build and has no fear of attacking. In fact, her attacking mindset may have been the most impressive of her many extra-technical assets.

On the other hand, her serve could use significant improvement, and she needs to tighten up her mental game—which brings us right back to the experience issue.

Stephens has been known to start slow, which is probably one of the things her new coach Paul Annacone has tried to redress. The No. 13 seed was all business tonight, punching through with a break in the third game, on her third break-point attempt. The clincher was a backhand service return that Stephens tagged for a winner right down the line.

But that 2-1 lead didn’t stand up. Svitolina broke back in the sixth game with shocking ease—the result of one of those puzzling letdowns that have always been a part of Stephens’ game. A pair of outright winners and a third-shot (return of the service return) backhand error left Stephens behind, 0-40. Svitolina finished off her own first break just like Stephens had, with a backhand down-the-line service return winner.

Anything you can do, I can do better. Svitolina caught fire in that game, and Stephens shrank back from the flame. Resorting to the familiar if puzzling passive posture that suggests that she has mentally checked out, Stephens allowed Svitolina to flex that attractive game of hers and run off four straight games, leaving her to serve for the set at 5-3.

But at that point, Stephens jump-started her game again. She build a 15-40 lead, then botched a service return, but made up for it with a magnificent inside-out forehand return winner to break.

It was at this point that the person we might eventually refer to as the “new” Sloane Stephens asserted herself. Instead of eventually floundering into a tiebreaker, she found her serve and hit three unreturned shots, sweeping four points to make it 5-all. She jumped out to a 15-40 lead in the next game, and secured the break on her third try with an unreturned, down-the-line backhand. It was enough to shatter Svitolina’s spirits, for Stephens served out the set with ease.

The youngster from the Ukraine could not shake her sense of a missed opportunity quickly enough to avoid being broken in the first game of the second set. But she rallied and pushed Stephens to two deuces in next game. Once again, Stephens unloaded on a down-the-line backhand to get to ad, and she smacked an ace to win the game and drive her advantage to 2-0.

That proved to be Svitolina’s last good chance. Clearly dispirited, she played erratically and never saw the break point she needed to get back on even terms. The closest she came was at deuce, when Stephens served in the fourth game. The most noteworthy aspect of all that followed was Stephens’ ability to keep firm control of the match as the girls took turns holding serve until Svitolina ran out of set—and match.

Stat of the Match: Svitolina broke the magic 50 percent success-rate mark on second serves, winning 15 of 28 (54 percent). But it wasn’t enough to offset her mediocre 62 percent success rate when she got her first serve in (23 of 37).